Crypto can be fiat and issued by the government, if the system remains status quo. Fiat is here to stay.

Until the government as we know it evolves at some point and we could also be using a system that we have not yet conceived.

Decentralized crypto and fiat (crypto) can co-exist, but the power that wants to control everything will try to do something about crypto they can't control.

Control can simply be guarding the on and off ramps and impose restriction through laws and regulations.

But the outcome will still be an inconvenient parallel economies for quite some time. As long as people want to use it, there will always be a system whether it is the black market, barter system, or the innocent trading the brownie points among friends and those who have those points (crypto)

Value is just what people believe, and to control crypto, there are many vectors to attack to weaken those views. Like through market mechanisms (paper markets - futures and derivatives), as we have seen in gold and silver, and now Bitcoin and Ether.