I read an argument, that proof of work needs to be useless and wasteful. If it would produce value in itself it would make 51% attacks more economic and thus the currency less secure.
The model breaks where work can be counterfeited (usually impossible) or where energy prices go to zero, which is why "bitcoin colonialism" was briefly a thing last decade. Much of bitcoin's design, this aspect also, is intended to protect against the bare-fanged, red-eyed money weasels it was also designed to attract.
Wrappers on candy don’t have value intrinsically but improve the quality of the candy.
Not totally convinced the analogy maps but interesting.
Still I do think there's some validity to the comparison. Fiat currencies are not backed by "nothing." They are backed by a state. Some percentage of the cost of operating a state is therefore "work" done to back the currency's value.
The question is: if we had a cryptocurrency backed by digital PoW that scaled to the level of fiat currencies (millions of transactions per second) and had some of their other desirable characteristics, would the state be able to proportionally shrink? That's what I'm not convinced of, but it'd be an interest experiment if we could spin up another universe and try it.
No, this is perfectly reasonable and catastrophically, dangerously inverted. We do not operate a state to generate money. We use money to fund the operation of the state. Otherwise we create a perverse incentive attracting what would be parasitism, had we not just incompetently surrendered effective beneficial ownership of the resource to the first sufficiently convincing comer.
Say, for example, the Afrikaner failson of a gemstone magnate, who is regrettably good at cosplaying a foolish person's idea of a wise person.