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.
So far I have not thought that in the future paper currencies will fall even though bitcoin will be the main means of payment for the public, and now if we look at some governments have planned to make their own coins like the government in China but I think they did not do it to avoid fall of paper currency but only to facilitate the public when making transactions.