This doesn’t make sense. Debt is money owed. So if money is “an accounting mechanism for keeping track of debt” then we have a circular definition.
Money can be completely separated from debt. And until around a hundred years ago — where gold was and had been money for hundreds of years — it was. A silver or gold coin is not anyone’s debt, yet it was used as money for centuries.
An excellent critique of the idea that money is created by governments was written by Carl Menger in his essay from 1892 entitled “On the Origin of Money”: https://is.muni.cz/el/1456/podzim2009/MPE_MOEK/um/8972262/me...
Menger defines money as, simply, “the most liquid good” — where liquidity i, essentially, defined as “how much value you lose when you exchange to and from a certain good”. For example, if you have a hundred chickens and you sell them in exchange for wheat, after which you immediately buy back chickens with your wheat, you will lose more value (chickens) than if you were to use gold as an intermediate commodity. This gives rise to a “common” intermediate commodity, because everyone wants to lose as little value as possible when selling/buying, and this intermediate commodity is money.
Of course, this has changed by now, since each country now issues their own currency and disincentivizes the use of competing monies/currencies through various means (primarily by defining their own currency as the “one true measure of value” by charging capital gains taxes on competing monies).
Anyways, even if it is non-coercive in the sense of having no West Coast Code or legislative coercive forces at play, you can still learn a lot about monetary economics in such environments. This author is interested in the emergence of monetary exchange, and that's a pretty big literature for instance, going back to Menger's "On the Origin of Money" (though Menger does note the later imposition of standardization from political authorities, etc.) and more analytical work such as Duffy & Ochs (1999).
This literature on the emergence of currency/monetary exchange from barter exchange typically understands such emergence to occur independent of any such force - all you need is the existence of the problem of double coincidence of wants. What I have in my inventory may not match what you want to trade for in your inventory, so some object that is marginally more "saleable" in the sense of being more widely desired, easier to carry, etc., will emerge as a currency standard. Also see Radford (1945)'s study "Economic Organization of a POW Camp" where cigarettes emerged as a common currency.