Here are three types of money:
- Commodity money: goods of value are used as money (e.g. gold in your example, or cigarettes in a prison),
- Representitive money: money is still based on a commodity but, instead of actually using that commodity in exchange, they use pieces of paper that can be exchanged for the commodity (e.g. the gold standard),
- Fiat money: money with no intrinsic value, which is trusted by people because they government tells them it will be the official medium of exchange into the indefinite future (e.g. the modern US dollar, British pound, Euro, etc.).
A fourth type that is emerging (e.g., in the form of Bitcoin) has no intrinsic value and no official backing from government. It is accepted in exchange solely because people believe that will be able to spend it again in the future.
The physical burden of physical money
Firstly, there is a serious practical problem associated with commodity money in its purest form, namely that transporting and storing the money is difficult and expensive. If I want to buy a house, am I supposed to work around with half a million dollars worth of "stuff" in a briefcase and hope nobody steals it? What if I want to buy a book from Amazon? Do I have to send them some gold coins in the mail?
At the very least, these considerations are going to compel people to use representative rather than commodity money.
The problem of debasement
Where commodity money has been used historically, it has been exposed to the problem of "shaving". Since the currency is intrinsically valuable, there is an incentive to shave a tiny amount off of each coin (such that the difference is indistinguishable from normal coin wear) and melt those shavings together into a piece of precious metal that can be sold. You can read more about this here.
Takes away some valuable policy tools
Imposing a commodity money would take from the government some valuable tools to deal with economic shocks. In particular, it reduces the ability of the government to use monetary policy to reduce the real effect of economic downturns. For example, during the most recent recession, major governments engaged in "quantitiative easing", which saw them creating new money to stimulate the economy. This would be much more difficult if creating new money meant having to dig a significant quantity of gold out of the ground of another country.
Additionally, it is not obvious how big/genuine the advantages you describe are. For example, here is a plot of US inflation:
Note that inflation tended to have higher peaks and be much more volatile during the first half of the C20 than in recent years. But that was exactly when the gold standard was in effect and the value of currency was directly tied to a physical commodity. Also, deflation was more common then, which is problematic because deflation has a number of damaging effects on an economy. Modern policy makers are better able to regulate the money supply to control inflation and keep it around the low and stable levels thought to be optimal.
People might be more willing to trust commodity money. But they would have to overcome concerns about counterfeiting and debasement. Recent experience from the last half century has been that people in stable democracies are, in fact, quite willing to trust fiat money.
Edit in response to comment:
It's true that precious metals are sufficiently valuable that large quantities are not needed to make most payments. But the problem remains that (a) if I am carrying them around to make payments then I am subject to a new source of theft/loss that is less acute with electronic financial balances; (b) insisting on a physical commodity money makes it hard to transact remotely (e.g. buying goods online or remitting money to pay for bills or an invoice); (c) businesses regularly need to spend, store, and move money on the order of millions or sometimes billions; often across borders or oceans. Moving from a world in which money can be stored and moved at essentially zero real cost, with essentially zero delay, to one where we are burning real resources to move physical stuff around would be a huge technological step backwards.
I don't understand what you mean about debit cards. Your whole question started out with "...not the version I always see mentioned (trading bills for gold at a set price). I mean having gold coins in circulation..." i.e. we are talking about commodity money, not representative money. Yes, debit cards fix the problem of physics, but they also mean we aren't talking about commodity money any more. Having a debit card you can hand to your bank in exchange for gold is really equivalent to having a US dollar banknote that you can hand in to exchange for gold.
Yes, the US dollar has lost a lot of its purchasing power. But that's a good thing! There are numerous economic benefits to a low (but positive) stable rate of inflation. Inflation per se is not bad, it only becomes problematic when we have either very high levels of inflation, or when the rate of inflation is not stable (both were true under the gold standard).