The question "How the cryptos will survive if all government bans it" has been asked often. I think the OP's question is interesting, because it makes us wonder about a hypothetical world where Bitcoin has replaced fiat. What would be the consequences? What would government look like in such a world? How should society adapt?
I've been thinking about a question for a long time... "Isn't it better, if the world accepts Bitcoin and alt coins, while the Fiat currencies system being totally canceled?" It might be a little bit silly, but this question always pop out from my mind
If you look at the history of Bitcoin, the reason why Satoshi Nakamoto created Bitcoin, you understand it was never meant to be a currency integrated into government. It was a rebellion against government financial policy. The purpose of Bitcoin is to change government, but currently government tries to change Bitcoin.