That might be come true ,that crytocurrency will replace fiat currency if the crypto will full activation and accepted worldwide, but I also think that it not totally replace fiat currency and fiat will be still be used in areas where there are no supply of internet access ,that cryptocurrency will be applied for .
But that is not an easy thing to for every government around the world to recognize and accept cryptocurrency due to certain interests which may be political or the policy might not work in the presence of certain existing systems like that of the central bank with is built around fiat. 
But lets suppose if crypto currency gets accepted by all the countries around the world, it will definitely give a huge blow to the demand for fiat and the medium of exchange will be cryptocurrency to a great extent.
It will be impossible. The people who do not want to recognize the crypto will always exist. Even if the government announces that the crypto is the main currency, they will start to protest against it.