I agree that the next century will be the time for cryptocurrencies, but I do not think it will totally and fully replace FIAT. The governments continue to exists, so they will not want to give up their power and they may come up with the crypto version of their crappy FIAT.
Cash money is almost out of use in countries like China anyways, and everyone else tend to use digital money based on fiat. Blockchain based cryptocurrency will have its own use, but as long as some people would like to have the monopoly of money to themselves, the government printed money, digital or paper, will live on.