There are bonds and stable currency issued peg to the defi or crypto world.
It would reduce the value but it's unstoppable.
See fei: https://fei.money/
Proof of work or hardware intensive proofs are only used in a few crypto currency so this is a very blunt response in regards to banning exchange.
I.e people will start directly using these currency for payments (which they already do) without exchanging to fiat. The stability is maintained by the defi collateral and shared acceptance.
So you would have to ban everyone to accept crypto currency and so on as payment but that is very catastrophic decision with large implications.
It also doesn't help crypto completely eliminates centralized authorities when moving across borders.
It's not solving much.
Without fiat exchange, People can only accept crypto in an economically feasible manner as payments up to the rate that they have expenses/outflows that can be paid in crypto. The price will only be able to stabilize at a price that is orders of magnitude lower than today. How much lower exactly depends on the health of the black market for exchanging with fiat.