If you are agreeing with me I don't understand why you call money a commodity. Money is only a commodity if it actually is physically a commodity, eg/ Gold or Silver. Paper money is merely a stand-in for actual value. It provides a unit of measurement that allows us to compare the cost of goods, services, or assets.
You could use any other commodity as a unit of measure also, ie Cigarettes. However, every other commodity doesn't quite have the attributes and properties that make up money or even better gold.
For economic modelling and theory everything is a commodity. You say you studied economics but perhaps they teach it different these days.
The key point about paper money being a poor substitute is primarily because the scarcity and store of value attribute - controlled/diluted by governments printing it at will.
I understand the point you are making but money is a commodity - by virtue of the fact governments control its supply and circulation and it is accepted by people. It essentially becomes a commodity.
Let's apply your approach to a Rembrandt. It's intrinsic value is cost of wood, paper and paint. How can anyone value it in millions? It too is merely a stand-in for actual perceived value to the holder. Because it is scarce its supply is inelastic. Because people have infinite amounts of money it's price goes up and up as people see it as storing value and as an investment. We are talking about the same thing here - a commodity paper with paint on it. I guess one could frame the dollar too.
How about product differentiation. Has no value other than one of perception. When buying a company one is buying the brands it holds. There is no intrinsic value in a brand other than one of perception and supply & demand. But those brand values are traded as assets the company holds.
How about 2nd life world. Players trade fictitious cyber-world items as commodities.
How about derivatives and so forth.
You can say zero doesn't exist why have it. What is the point of giving nothing a name if it doesn't exist. Because with zero numbers fall into place. Same with money as a commodity.
You need to consider money as a commodity. Same as gold.
When you see it as a commodity you can then price it. The price of that commodity is then determined by the market by supply and demand. It is not just an arbitary unit of measure created by governments as to what their money is worth. You can see this all around us as people switch commodities.
You pretty much asked the same question re:Zimbabwe printing money. However, US money and Zimbabwe's money is not the same. Because they are currencies. Currencies are commodities too. Because they are commodities they can be priced accordingly. Because we are exchanging commodities against each other their rate of exchange is different based on supply and demand.
Hope it makes sense.