I believe that while cryptocurrency can not replace or oust Fiat. Because I do not see problems that they both existed. So that you can freely transfer from cryptocurrency to fimt and vice versa.
Don't you really see the problem with fiat? There are a lot. Essentially Bitcoin is here not to replace fiat but it could happen in the future anyway. Many Bitcoin supporters want to replace fiat with Bitcoin, this is why questions like "Why fiat should be replaced by Bitcoin" or "Why is it better to use Bitcoin rather than fiat" are very popular among Bitcoin community. Bitcoin is used by few party as a tool to fight against government in order to replace centralized system. However, Bitcoin can always live together with fiat and no need to force it to be a main form of payment, let's just wait which will die first and which will survive.