It could replace fiat if the price is stable. However.. only if it replace fiat.. it will become stable. I foreseen many physical shops with 'Accept Bitcoin' in the next 20 years or so.
Altough the price is stable I think bitcoin can't change the fiat because no one can control it, higher or lower it depends on us that do the trading at most. Its true that now many people accept bitcoin but in the next 20 years I dont think people will do that again, but this is just my assumption. It still being polemic between bitcoin and many things out there