The cryptocurrency couldn't really replace fiat currency because fiat was supported by the government and fiat money started to dominate since the 20th century, that is why it is being used globally. We also do not need for cryptocurrency to replace fiat because cryptocurrency should always be decentralized.
It is not that it is supported but it is the currency being controlled by them. They would never let crypto currency replace fiats since we all know that cryptos are decentralized, as no one would control it, whales would be able to manipulate it. I think crypto currency would go side by side with fiat, as we can use fiat every day, that would be the same as crypto currencies.