Taxes explain why people want a certain kind of money---that is, why in the US we carry dollars, and in the UK people carry pounds, and so forth. I'm less familiar with monetarism (i.e., Friedman), but I think the big difference between monetarism and MMT is that the former operates on the idea that money is a store of value, while the latter says that money is a unit of account and transaction medium.

To clarify this a bit, by a store of value, I mean that monetarists take money to represent, say, an amount of labor. It's a very "bars of gold sitting in a vault" way of thinking about money, and it very much leads to the conclusion that price stability (low inflation) is the ultimate good in a monetary system. However, it also leads to the belief that money becomes "diluted" by issuing more of it---that is, it's based on the likely false belief that issuing more money causes existing money to become worth less.

MMT instead pulls from a tradition called "functional finance," which holds that the "right amount" of money is the amount that would be required to purchase all the goods that could be produced in an accounting period, given a frequency with which that money is expected to be spent. This gets away from the belief that money is a store of value, to a more functional view, that money is a thing that exists to facilitate transactions, and that there is both such a thing as too little and too much of it. That is, having too little money to buy all things that could be made instead means that the deficit---the things that can't be bought---instead just won't be made.

Regarding kids trading cheetos, I'd reiterate my argument from another post: taxes are a constraint on what forms of money can be used. If such a constraint isn't in place, for example, when considering black markets, or when considering elementary school children, then it stands to reason that people will tend to agree on what's most convenient to use. Taxes serve to limit the options available---using anything but the sovereign currency for transactions that are taxed (directly or indirectly) usually carries too high a cost, but when considering a simpler economy that contains no taxes, then anything could fill that void.