I think the parent is talking about chartalism (
https://en.wikipedia.org/wiki/Chartalism), which is essentially the idea that fiat currencies derive their value from the fact that taxes must be paid in them.
A sort of "just so" story about this would go something like (with much credit to David Graeber):
"Way back when, some Assyrian king got the great idea to, instead of giving their soldiers food and drink, give their soldiers tokens. They would then demand a certain number of those tokens per head from their subjects. Suddenly the tokens have value, and the subjects are put to work selling goods and services to the army."
I'm not an expert on this theory, but there are potential oddities, similar to your points:
* This would suggest the value of the currency is closely tied to the total taxation. (Why, for example, is the Swiss Franc highly valued by investors outside of Switzerland?) I guess you could validate or invalidate this by looking at whether the ratio of M2 to annual tax revenue is somewhat fixed (across currencies) or quite fluid?
* This fails to explain currencies which retain value after they are no longer in use by a central government (as with the Somali shilling, as noted in the Wikipedia article) or, indeed, Bitcoin.
Personally, my sense is that chartalism is correct as an explanation for one way to bootstrap a currency, but clearly (as Bitcoin shows) is not the only way to bootstrap a currency, and once you create a level of reliable demand, you no longer need it (hence the Somali shilling or, perhaps, the high valuation of the CHF outside of Swiss taxpayers).