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 will not fully control cryptocurrency, but both in the future will co-exist, in other words, most governments in the future will be able to accept digital currencies to be used as alternatives for various transactions without having to eliminate the fiat function itself