Folks would trade bitcoins with other cryptofiat coin's. Governments would have the best of both worlds and bitcoin becomes the defacto reserve currency.
Or the de facto killed currency.
"You are in the Eurozone and you insist on being paid with something else than Euro? What is wrong with you? Maybe I should call the police."
Exactly my point. If everyone chooses a cryptofiat of their own, nobody will accept anyone else's as legal tender. They will have to exchange them at the border. Rather than pick one nation like USA to be the reserve currency so they can enjoy all the benefits of that status, why not a neutral gold-like cryptocurrency?