Why is it that we must make sure banks don’t fail? Why not let them fail like anything else forcing people to diversify where they put their funds and providing impetus for banks to be more responsible simply to survive like any other business? It would moreover lead to mega banks potentially separating into smaller, more manageable, banks in the cases where they have exceeded their reasonable span of control
First, when it comes to policy we do not ever need to do anything. Most governments want to avoid catastrophic economic consequences that come with widespread bank collapse and that's why they are trying to make sure banks don't fail but as long as in your personal cost-benefit analysis costs of bank failure do not outweigh perceived benefits there is no reason to do anything.
There are several reasons why bank failures can have significant negative consequences:
Large banks are often systemically important. A systematically important bank is a bank that is so large or interconnected that when it fails either due incompetent management or due to negative idiosyncratic shock (i.e. bad luck) it triggers financial crisis. Financial crisis in turn often leads to collapse of other banks even if those other banks did not had bad management or luck (see FSB for examples). In fact some of these are globally systemically important meaning that even a bad shock in a single country housing one of these could trigger global financial crisis that would affect even smaller foreign banks.
Modern banks, besides their business of lending and investing, also provide 'financial' infrastructure for the economy to operate. When multiple banks collapse at the same time this financial infrastructure collapses with them.
In a current monetary system banks create portion of a money supply through lending money. When banks collapse, money supply tends to collapse with them. This can trigger terrible recession, in fact this was what caused Great Depression (see Friedman & Schwartz Monetary History of the United States). This is because decline in money supply is contractionary, so doing that during recession makes things just worse.
Although central bank can intervene to try to prevent such collapse of money supply, it would have to do that through providing liquidity to banks, like Fed did in 2009 which helped to prevent another Great Depression (Bernanke 2009). This is however de facto 'saving' the banks instead of letting them fail, so under your proposed alternative there would have to be money supply collapse and Great Depression like recession.
Moreover, some of your proposed benefits are quite unlikely. Even if banks are allowed to fail:
it is dubious to think that it will completely solve the moral hazard issue. People might learn to diversify and keep several multiple accounts in different banks, but from individual perspective it is difficult to asses credibility of a bank. When regulatory agencies try to asses credibility of financial institutions they have whole teams and even they do not always manage to do good job because modern financial institutions are quite complex.
Moreover, as discussed above, when systematically important institution fails it can easily trigger failure of other banks that perhaps did not mismanage their business, have been conservative in their operation and did not had bad luck.
The reason why large banks exist is primarily due to technological progress. Modern computing creates large economies of scale where a bank will have large fixed cost of establishing all computational infrastructure and very small variable costs (Pulley and Humphrey,
1993, Sealey and Lindley, 1977), especially now that banks are moving all business online. As a result banks are growing large because it is simply economically efficient for them to be as large as possible. So this would not necessarily make banks smaller.
Of course you would be correct to say that financial regulation can contribute to making banks larger by creating barriers for entry, which prevents smaller companies to enter and establish themselves. However, I think any reasonable economist would say that the economies of scale are the primary reason. Hence, deregulating the industry would not necessary result in smaller banks.
Moreover, some financial regulation can keep banks smaller. In past banks were kept artificially small by the ban on interstate banking.
How would increased regulation - which just finished failing (again - https://www.wsj.com/articles/how-bank-oversight-failed-the-economy-changed-regulators-didnt-7dbb842d) be a good response? It is only going to obligate banks to less efficiently allocate scarce resources (money) by mandating how they will mitigate risks and if history has taught us anything at all banks will look for a way to circumvent said regulation. (https://www.wsj.com/articles/it-is-time-to-admit-it-bank-regulation-doesnt-quite-work-9617d913).
The reason for this regulation is to make sure that banks need government assistance as little as possible. No amount of financial regulation will ever completely prevent bank failures. Similarly even though air safety regulation makes planes the most safe mode of transport, planes still crash from time to time. The point of this regulation is simply to minimize number of times banks fail and ask government for bailout.
You are right to point out that this regulation also has its cost. We do not really have long history of modern bank regulation. Banking was quite deregulated prior 2008, and modern regulation that came in place after that existed only for a decade or so, and hence it is difficult to definitively say whether this new regulation, in long run, mitigates moral hazard and other issues sufficiently enough that the cost of this regulation outweigh the benefit. However, many, if not most, experts believe it will be worth while in the long run.
Even if they are wrong, its very doubtful letting banks fail would be solution. More likely if these issues of moral hazard cannot be fixed by regulation we would have to move to different monetary system like the Chicago plan or something along those lines, because I doubt any society will be willing to stomach the consequences of a systematic bank failure, and only 100% fool-proof way to prevent that is to move to full reserve system.