I don't think there's ever going to be a world in which we don't have fiat, and we only have Bitcoin.
The reality is that it's going to be much more complex than that. We will have Bitcoin living in parallel with fiat currencies.
Even right now there's some people living in a Bitcoin standard. They get paid in Bitcoin and they pay their goods and services with Bitcoin. Others have massive amounts of Bitcoin and they simply sell a portion of it every month to live off Bitcoin. On the other hand, there's plenty of people that live in a 100% fiat world and have no idea about Bitcoin.
Just like the Internet, the people that use the new technologies will get ahead, and the people stuck in the past will be worse off.
Exactly. Governments simply won't allow that to happen. Otherwise, they would lose control over people's financial life. Bitcoin will only remain an alternative currency for those seeking true financial freedom. The fact that it can be used anywhere there's access to an Internet connection, is more than enough to classify it as a "world currency".
Some governments officially recognized BTC as legal tender, while others are banning it completely. Yet, Bitcoin's decentralized and censorship-resistant design makes it immune from governments' actions. It will certainly live alongside Fiat for generations. Who knows how far Bitcoin will go in terms of mainstream adoption worldwide? Just my opinion