I think fiat will still be there even if cryptocurrencies might become global currencies. Fiat will still be used for local transactions and for daily transactions.
I dont think that this will remain the case forever. Like in history, first there was barter system, then gold coins which was replaced by paper money. With the changing time and needs, revolution comes in every aspect of human life. Now the world is becoming more technology oriented so digital currency will overtake the present money and it is future.
as long as bitcoin doesn't have clear founder data and official offices, they will never get recognition as a currency, many countries worry that bitcoin will be the cause of economic warfare because there is no central position in regulating price policies, this will make the economic turmoil return to the era barter.
Fiat will remain in place, but in the future, their functions will be far more prospective to be used in digital systems, so I think eventually they will continue to join crypto, but still with their own altcoins.