Crypto is absolutely capable of doing it and I don't actually doubt that it will replace fiat one day, fiat can't fulfill all the needs of todays community.
Probably cryptocurrencies can not replace fiat. The entire world economy is based on fiat money. Krypto is still too small a part of economics, and despite gaining popularity, it will not become a significant element for a long time. In addition, cryptocurrencies would have to be regulated by law and centralized, and the entire market would have to be stabilized.