tl;dr this would not work in either closed or open economy unless your proposal would include very large cuts to current social and welfare spending as only arguably small part of those could be funded that way. There are several reason for including:
there is a limit to the amount of real government spending that can be financed by monetary expansion. For redistribution you care about real spending not simply monetary transfers. If a poor person gets transfer of $\\\$1000$ but one apple costs $\\\$10,000$ then such person is much poorer than a person getting transfer of $\\\$10$ when apple costs $\\\$1$. Even though people who first get to spend these money might initially get a seigniorage revenue from it - the amount of seigniorage is not enough to provide anything close to current level of real welfare transfers. Unless you envision some sort of society where welfare/redistribution spending is only about $10\%$ of what governments currently spend it would have disastrous consequences while not improving lives of poor by much.
Open economy considerations actually generally make the situation even worse. To be more specific they might lead to bit better situation to economically large countries that also issue reserve currency but empirically speaking most countries in the world can be characterized as small open economies that do not issue world's reserve currency.
UBI is actually not generally considered good redistribution policy as it wastes resources so choosing UBI specifically as
opposed to some non-linear system of taxes and transfers would only
make the above worse.
Full Answer:
What can theoretically work depends on theory you want to follow. Time dilation works under the Einstein's general relativity but does not work in classical Newtonian mechanics. I will assume you want to follow contemporary mainstream economic theory. Under mainstream macroeconomic and public economics theory government cannot finance itself without taxes and even if it could monetary policy is bad tool for redistributing resources.
First thing first, we actually don't need to imagine this "centralised pseudo-cryptocurrency where only the state can create new currency units". This is how modern fiat money already works. Most money is already digital not paper and even with paper money costs of production are so minuscule that only in rare extreme cases (such as recently in Venezuela) government faces any limits on the amount of money it can create. So we are already living in a world where governments can do this. Of course, I am not trying to suggest that 'crypto' is exactly same as fiat currency because of the ledger, limitations on supply of 'crypto' and because demand for private crypto cannot be generated by taxes (as that would undermine government monopoly), but for the purposes of this particular question there really isn't meaningful economic difference.
However, redistribution and social spending in general, even at the current level that some people consider low, comprises of approximately $20\%$ of GDP on average across OECD countries and hence requires a lot of resources. Furthermore, it is generally agreed by economists that government cannot finance any amount of real spending it wants through money creation. You can see this from a results o a IGM forum poll, which is a poll among wide and diverse group of top economists, showed that most of them disagreed or strongly disagreed with statement: "Question B: Countries that borrow in their own currency can finance as much real government spending as they want by creating money." (where real spending is what arguably matters for redistribution the most) and once weighted by their confidence the poll showed that they all disagreed or strongly disagreed. So there seems to be strong consensus among the experts that what you suggest is not possible/desirable. Now the question that still remains is why is it so, I will start explaining that in next section from the point of view of closed country and then quickly discuss some additional reason in open country case.
Closed Country Macro Reasons:
First and foremost reason is that this would generate massive amounts of inflation. The relationship between money supply and inflation is determined through money market equilibrium (see Blanchard et al Macroeconomics an European Perspective or for shorter explanation Mankiw's Principles of Economics) which can be in its simplest form described by the equation of exchange:
$$MV=PY\implies P= \frac{MV}{Y}$$
where $P$ is the price level - change in which is inflation, $M$ money supply, $V$ velocity of money (number of times a unit of currency is used in economy), $Y$ is the real output. This relationship implies that conditional on keeping output and velocity constant increase in money supply will lead to increase in prices and hence inflation. The reason why we can hold $Y$ constant is in the long-run independent on amount of money in economy, because while in short-run monetary expansion can stimulate the economy, the $Y$ is ultimately determined by what the production capacity of our economy is. If we have only $100$ units of labor $L$ and we face production function $Y(L)=\sqrt(L)$ then society can at best produce 10 units of output irrespective of how much money there is in the economy (even though the productive capacity can increase thanks to economic growth - this does not again depend on amount of money in long-run). The reason why $V$ can be hold constant in the long run is that velocity depends on how fast are people spending money they get. Stuff your money under mattress and forget about them - velocity drops. Spend/invest them as quickly as you get them velocity increases. Velocity definitely changes in the short-run for example during recessions it drops and increases in expansions. It can also be offsetting $M$ in liquidity trap. However, while it might be in some periods low and other high on average it won't change much in the long run. As you can see from FRED data if we exclude the current corona crisis the velocity of $M2$ is historically quite stable over long periods of time even if it can change significantly in short run.
As consequence in the simplified model above holding $Y$ and $V$ constant government can't really redistribute any real resources to the poor just by monetary expansion. However, I on purpose always emphasized that the above is an over-simplification as it's just an undergraduate version of the model which lacks some important nuance.
First important caveat is that the above model does not showcase the dynamics of the relationship between money supply and price level increase. The fundamental reason why more money leads to higher prices is that people take that money and spend it which bids prices up. Hence if there is an unexpected increase in money supply the first person can spend this new money at prices that do not fully yet account for increase in money supply. Hence government by issuing money gets a seigniorage revenue - which could be in principle transferred to the poor. However, a problem is that amount of real spending that can be generated in this way is quite low. According to Haslag (1998) the seigniorage revenue most government generate is below $2\%$ of GDP - a far cry from average OECD social spending of about $20\%$ of GDP.
Furthermore, an important thing to keep in mind is that when people do expect certain level of inflation they will just start accounting for it in their contracts (see again Blanchard et al. or Mankiw textbooks mentioned above). This occurs especially at higher levels of inflation and for these reasons in your proposal (which would arguably generate at least 2 digit inflation) you would have to eventually always unexpectedly increase the money supply at increasing rate not just some fixed $10\%$ in order to create new 'surprises' for people which would lead to ever increasing inflation.
While economists generally advocate for positive levels of inflation (see this answer on Economics.SE). Most economists agree that the level of that inflation should be somewhere around $2\%$ per year on average over business cycle as high inflation rates have negative effect on economic output due to for example menu costs, shoeleather costs, increases relative-price variability and the misallocation of resources or other problems (see again Blanchard et al. or Mankiw). In addition inflation also redistributes resources from savers to lenders in a way that has nothing to do with them being rich or poor. Even if it could be argued that on net poor people are more indebted it would be terribly targeted measure as it would redistribute resources away from those poor who aren't.
Second, modern advanced economies experience on average approximately $2\%$ economic growth per year. Hence, money supply can be increased by that much on average without any effect on inflation. This would give government again some extra breathing room provided that you want to keep the level of social spending constant. However, again this would be just pennies compared to the amount of social spending and redistribution modern governments engage in. Furthermore, this is to some extent moot point as arguably even if countries would want to keep relative social spending on constant level they will tend to increase the absolute value over time as our economy grows.
Third important caveat is that more complex models for example show that at zero lower bound (ZLB) velocity can offset money supply expansion leaving inflation unaffected and in more complex models expectations of what the money supply and other variables will be rather than what they actually are plays bigger role (see Krugman 1998).
As a result in certain times government can pay for more of it's real spending through monetary expansion without creating inflation while in other times its ability to do so is more limited. However, this creates an additional problem since poverty & inequality is here always not just in a certain years. Hence, if government would rely solely on monetary expansion for welfare spending while trying to keep inflation down poor people would face unpredictable welfare transfers which would lead to host of other problems - e.g. how do you choose which place to rent if your welfare payments change over unpredictable business cycle?
To sum up, doing some back-of-an-envelope calculations we could reasonable argue that given the above caveats in mind government could finance at most about $4-5\%$ of GDP worth of real spending over business cycle (and even here some might say I am being too generous), but that is nowhere near of how much average government needs for redistribution policy. Hence proposing to finance all welfare spending that way would require for most governments to drastically cut their current social spending.
Open Economy Considerations
Open economy considerations would not change that much. A country which has an advantage of issuing reserve currency will face little a bit less constraints on how much real revenue it can get from monetary financing. However, generally speaking, political reasons aside, reserve currencies become reserve currencies because relative to other currencies they tend to keep stable value so this advantage cannot be abused too much.
For open economies that are not so lucky, especially for small open economies, there would arguably be more additional problems than benefits. First, such monetary expansion in open economy will result not just in inflation but also exchange rate depreciation.
Exchange rate depreciation can be helpful to an economy to certain extent as it helps to boost exports, but this cannot be done indifferently as over long periods of time trade musts balance and hence country cannot just keep being net exporter forever (See Krugman et al. International Trade: Theory and Policy). Furthermore, in some cases economies can even experience contractionary devaluation (See Krugman & Taylor 1978).
Next as discussed in previous part in more nuanced models inflationary expectations matter as well and those in turn can depend on exchange rate (See Mark International Macroeconomics and
Finance: Theory and Empirical Methods) . If inflation expectations are weakly anchored and exchange rate depreciation can 'trigger' higher inflation expectations then that would make problems discussed in previous section even worse.
Furthermore, small open economies are at high risk of dollarization or more generally currency substitution (in recent history it was mainly substitution to dollar). This occurs when people within the economy decide to stop using the government issued currency, and it happens mainly due to local currency quickly loosing value, and switch to another one (see Copeland Exchange Rates and International Finance for more nuanced exposition). The whole phenomenon of currency substitution shows that the store of value property of money is far from trivial. A currency substitution basically eliminates even the small seigniorage advantage that was discussed before.
The above is not exclusive list of differences for open economy but I think that at this point this answer is getting bit too long and you can find further arguments in the sources I cited. I think the literature can be sum up in saying that for open economies that are big from economic perspective and enjoy special status such as being the issuer of reserve currency can be better off but in no way so to allow government spend up to $20\%$ of GDP or even close to that. On the other hand small open economies will face more disadvantages, potentially even leading to a situation where their own people will decide to not use their currency anymore and substitute for some another one.
UBI Would Probably Make the Above Worse
UBI is not generally considered very efficient way of transferring resources. This is because even though UBI distorts the incentives of people between being economically active or not to lower extent than let's say combination of non-linear taxes and transfers, it is due to the universal part very badly targeted welfare measure. Most economists think the disadvantages of UBI outweigh the advantages and hence relying on it would probably make issues worse than if you would just follow some non-linear transfer scheme (although here the consensus is far less clear cut). I won't be going into detailed theory behind UBI because I think that is mostly tangent but as this another IGM forum poll on what top expert think of UBI show most economists think it's not good welfare measure.
The issue why UBI is not desirable can be explored more in various literature review papers such as Hoynes and Rothstein (2019) or Martinelli (2017) and sources cited therein. The literature can be summarized nicely by the following quote form Martinelli:
an affordable UBI would be inadequate, and an adequate UBI would be unaffordable.
However, I on purpose added probably to the title of this section as literature on UBI is not fully settled and it is of active research interest. Especially in recent times we actually can see some real life UBI experiments while in the past research mostly relies on theoretical and numerical modeling.
