Fiat and cryptos will coexist for more time to come without a doubt. But with technological advancement it won't remain the case. We will shift to better and more secure payment methods and then fiat will go away automatically. We might even see better paying mechanism than cryptos as well.
Fiat, like cash, may someday die, but this will not happen soon, and it is not yet known whether it will ever be at all. However, in any case, the national money of the states will always exist until there is only one super-state or alliance of states on the Earth that create their own currency like the European Union.
Until this time, the cryptocurrency will go in society with fiat.