If it were the case that the main currency of every country in the world is Bitcoin. Then how do you think the world economy would be run? Because when Bitcoin becomes the main currency, the American dollar and other countries will have Bitcoin as their main currency. The local currency of that country will be associated with it as the second currency. In this case, how would Bitcoin be used or how can it play a good role in the world economy?
The world might never have a single government because there is no single government. The United Nations, which was created to promote world peace, has failed to achieve it. I doubt if Nations will come together and accept Bitcoin as a legal tender.
Fiat will always exist because it has its advantages. Bitcoin will always need the Internet and at least a smartphone for transactions. There are people who don't have such facilities, so fiat will be the only option. Bitcoin will always be an alternative to fiat.
We shouldn't also be deceived that Bitcoin will improve the economy of any nation. A nation can still be poor even when Bitcoin is a legal tender.