I think that fiat will not be able to completely disappear even in the distant future. Many people love to diversify their funds and they will still hold some of the money in the form of paper money.
I agree because majority of the people around the world still prefers fiat over cryptocurrencies because they are more convenient at it. People need time to study the use of cryptocurrencies like bitcoin before they start using it. This new technology is more risky and more volatile than the ordinary fiat or money that they've been using and it also requires knowledge in internet to be able to perform a transaction.