Someone help me out here, am I missing something?

Proof of work = money is backed by an intrinsically valuable and scarce asset (electricity, compute power, etc.)

Proof of stake = a coin is only backed by itself, is not produced from a scarce asset with intrinsic value, and usually has no cap on supply making it inflationary (e.g. WEFereum).

So... how exactly is proof of stake any different in a real sense from fiat, aside from not being issued by a government? Seems identical in every other aspect.