It’s a question of the most stable thing to use to mediate value for exchange of goods and services, right? Fiat currency is just the choice of “the state” as a stabilizing force. Certainly it’s better than trusting the scarcity of rare metals, but eventually “just trust the state” will become a problem, and we’ll need to think about rebasing currencies. In theory, computational complexity isn’t a bad choice, but nobody has come up with a solution that actually functions well as a currency.
But I agree, the finite planet has nothing to do with any failings of fiat currencies, and only makes sense as a failing of the “number must go up” mentality endemic to capitalism.