The problem is different to the real world in that there is a penalty for holding small denominations in the real world - they become difficult to hold and use. Similarly there is a penalty, well difficulty, in acquiring a large proportion of all the larger denominations.
In order to freely exchange denominations, everyone had to be confident that they won’t become scarce. But if a wealthy group could capture a large proportion of the smallest denomination, it would cause problems for everyone else (and ways for the group to profit from that). So there is an incentive to do this which is not present with fiat money.
I think the key to any multiple denomination scheme is ensuring that denominations are readilly exchangeable at negligible cost, and the issue I’ve highlighted would need to be solved. Otherwise I’ll grab loads of the smallest denomination and force you to pay double if you want any.