I think that there is still a need for Fiat money, because not all countries and people are adapted to cashless payments.
Ask a thousand of random people what they know about the cryptocurrencies. I bet, maybe 20 of them or even less will give you the right answer. Most of us still believe in fiat more than in the crypto.
Till date fiat currency is necessary for a country because without fiat currency a government cannot run. But I am sure after taking over the market by cryptocurrency the role of fiat will finish and governments will no more need for fiat currency. All the transactions make by big companies and government departments in fiat currency will be replaced by cryptocurrency.