I don't think that cryptocurrency will replace fiat currency in future. Cause we can't think our daily life without fiat money.
Right now we can't think about it but we're going to the golden age where transactions will be digitalized. It's either crypto's are going to be innovated by an agency of a government that can be in favor of them or they will just use the technology (blockchain) together with digitalized fiat money.
The cryptocurrency will replace fiat money it is only a matter of time. It is necessary to wait 5 years and everything will be.
5 years? I don't think that's enough for the world to start using crypto's as main payment method for everything. They can adopt the idea of crypto's but they won't fully rely to it.