Cryptocurrencies appeared only few years ago. Fiat money exists few thousand years. But I believe that in 5-6 years fiat money will be replaced by crypto in developed countries.
Revolutionary payment methods rarely are introduced. The credit card was invented in the late 1950s. It took the invention of the debit card before card payments saw widespread use. Card payments surpassed cheque payments in the 1990s.
https://www.marketplace.org/2011/08/18/business/news-brief/short-history-debit-cardIt will take a combination of promotion and innovation before cryptocurrency will see widespread use.