Currecy that depend on fiat anyway can't replace it, and bitcoin also can't become fiat currency, cause in many countries it's still illegal for using.
I think fiat will always be fiat, like we know it today. I don't think much will change about it. I just don't think bitcoin can replace fiat. The only way this would happen is if all the governments worldwide would adapt to it. Which I doubt that they would.
Governments will never support bitcoin, they will support only their local currency they don't want to loose their control on the money and they will never allow bitcoin to be a primary currency.