I don't think that really stacks up. A lot of the really interesting research into non-mainstream monetary theory (i.e post-Keynesian/modern monetary theory) is saying the opposite - that the size of the money supply is actually hugely important, and not having enough at certain times has caused as many problems as other times when there has been too much.
The money supply really needs to be flexible to account for the amount of goods and services produced by the economy. Too much and you have inflation, too little and you get stagnation.
So I don't believe that a currency based on a fixed supply of money would ever actually be workable long term (and unsurprisingly gold and other commodity backed currencies have never lasted).
Not suggesting merits of either system. Just saying that if the supply is not based on some gold standard scheme, then for all intents currency is just paper when it's printed. It assumes value when paid in wages, loaned, etc. Effectively, it has to be laundered. The middle class is best at laundering because their ratio of earning power to debt to spending power. If the middle class shrinks, a money system that depends on it will lose value.