I don't think so because fiat is already existed for a long time and it helped maintain our economy. Unless we find better currency than fiat, it is too difficult.
People talk about Cryptocurrency taking over Fiat currency. Today this is not possible, because still a lot of people prefer their Euros instead of a online coin. Let me give you a example old people now prefer to invest in Gold and silvers, because they are used to it.
No this cannot be possible at all this is because Fiat currency is being used by all the people of the world.All the transactions all over the world are done through the Fiat currency only.It is accepted internationally.It is also backed by central banks and governments as it is centralised.It can be used anywhere and anytime unlike some digital currencies which require internet connection and some basic knowledge to get operated.Fiat currency is established from the traditional time period.