but that's the crux of decentralized currency's raison d'etre, is it not?
In theory - yes, in practice - crypto is most commonly used as a form of investment, so the ability to exchange it for fiat/other goods is crucial for that purpose.
It still has the potential of becoming fuel for an alternative economy if the traditional fiat system gets overly restrictive, but that won't be easy to achieve.
unless it becomes impossible to simply give central bank currency to other people without even the slightest risk of the transaction being delayed and/or reversed, exchanging said currencies for Bitcoin (or whatever else) will always be possible, whether the so-called authorities like it or not
Banks already have systems of flagging suspicious transactions, plus, high penalties for illegal/unlicenced P2P trading could make it simply too risky for the sellers.
in a world where that becomes truly impossible (at least in practical terms, and we're for sure getting closer to it), the actual currency itself loses it's status as well as it's value, because it is not a meaningful means of exchange any more (which is far more serious than simply losing relative value to other tokens for trading). It ceases to become proper money in the most fundamental sense, and it will hence be rejected by those who should apparently be subjected to it
one way or another, the instrument with the best money properties will win out.
Sure, but this rule only works when you have the freedom to choose an alternative to such failed currency. In a scenario where crypto trading is delegalised, I can't imagine it replacing fiat, even if the use of fiat is massively restricted. Especially if fiat is still good enough to use for the purchase of government-approved goods.