I really doubt our fiat will be completely do away with, but am sure they will in gbe future be limited to local daily transactions and transactions that arr not very heavy. Cryptocurrencies will be use across borders and inter-states within country. To achieve a truely cashless society wherein transaction failure rate is kept almost at zero, we need the digital currency. We really can't continue with the gangster like style by which these economic cartels manipulate money to their advantage.
I agree, its been ages since fiat is the source and main currency of all the countries worldwide, honestly I think cryptocurrency cannot remove or takes place fiat. Cryptocurrency can only help the economy of each country, it can help people also with their daily lives, similar to dollar and local currency, dollar remittance help the country grow by converting it in local currency same as in crypto to fiat, if I am not mistaken to this one.