Fiat will be replaced by crypto currency but i dont think it will be bitcoin. Government want to control everything and even fiat money , bitcoin cant control by the governement so they will create thier own and will use blockchain technology to make a new way of payment before fiat currency fall.
The government rejecting bitcoin to be the one who beat fiat currencies and totally replacing it is reasonable but the possibility that the government will change and will see what benefit bitcoin gives us compared to fiat and any other payment method in the world now is really big. There is still a lot of time for the government to consider it so I really hope that if fiat will be gone I hope that it will be cryptocurrency who will replace it.