Surely the government won't allow it to happen because they'll go bankrupt if everyone moves to Bitcoin.

Let's say the said scenario happened now, once billions of people starts using Bitcoin the network will be busy due to the millions of unconfirmed transactions and fees would go up (btc wise). The price could be a problem for some people because of the volatility, though it's expected that the price will stabilize as soon as more people are trading Bitcoin. I still think that there will be times that all of us have to spend more/less.