It will never happen that people will lose their trust to the government, otherwise the world will be in chaos. We might see the crypto adoption will grow significantly, but I am sure, we still have a government that will govern its people and we are all oblige to follow the law of the land.
There will be government in some way, but crypto have a technology for a government itself it is called DAO. The way how things stand right now is that people who are in the system just don't want crypto to adopt in the bigger scale because they're or their families are profiting in a big way from this system. Looking for a crypto-only economy will lead most probably to gaining as much power from them as they can to be still on the leader position.