No way people will always trust their respective governments to a certain extent.
There is a big possibility that cryptocurrency might replace fiat in the near future, our technology is evolving and having fiat in the near future seems too old for a bigger technology, and that is what the majority wants, to have cryptocurrency as the currency that we are going to use in the near future for more convinient and for the new experience that we could have on using cryptocurrency as the new fiat.