I do not know if the world is ready to sacrifice their "precious" Fiat currencies and to replace it with something that are not under their control. Every country value their local Fiat currencies and they do anything in their power to manipulate it's value to attract other countries to use it.
The US Dollar has lost most of it's value, but it is manipulated to reflect a image that it is very stable and also very strong. This is why a lot of countries are using it as a Global Reserve currency.
You might be right. Governments wouldn't give up Fiat that easily, especially when they'll lose control over people's lives. Something they can't manipulate to their own will, would strip them off the economy. For this and many other reasons, it's very unlikely Fiat will disappear in the future. Bitcoin may be a good, decentralized alternative to Fiat, but it won't be able to become the "global unit of account" if Fiat is still in play. As long as governments have their own Fiat currencies, Bitcoin won't be going anywhere.
I think there's no need to worry about this, since Bitcoin wasn't made to replace Fiat in the first place. It does its job pretty well as a decentralized financial system anyone can use worldwide. With how things been going lately, it looks like Fiat and crypto will co-exist for generations. Just my thoughts