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.