no, this process will ruin fiat economy and politics will never tolerate power lose.
It will possibly happen in the near future if the world is fully run by computer, but as of this time maybe it will never happen due to political activity and the game of life powers, and also the world today is not yet ready to make that happen because of every country's economics standing is not the same.
I dont think so that in near future cryptocurrency will disappear fiat completely because cryptocurrency would be fully introduced across the world when all the worlds population are provided electricity, knowledge, computer and internet facility and mostly population of the world are deprive of these facilities still.
No doubt that in developed countries cryptocurrency is getting fame and it has suffered upto some context the fiat. Everything is possible in the world and may the time come when fiat will disappear due to extreme involvement of people in cryptocurrency.