I dont think bitcoin can replace fiat money. Fiat monetary standards enable the government to have a lot of control of their economy.
They can choose to print progressively or remove some from the economy through banks. A cryptocurrency would need to be connected to their fiat cash and be absolutely controllable, for a government to permit it instead of their fiat, however that would essentially be a fiat at any rate. So we would require new enactment or new governments.
Bitcoin will not be able to replace fiat money, because banknotes are easy to use for payments and there is a physical form. For example, can you imagine school children using bitcoin? It will be difficult for small transactions such as buying candy, ice cream, buying pencils, etc. But for large transactions that use banking services can use bitcoin, because it is faster, easier, and cheaper. So bitcoin and fiat money can function together as a means of payment.