Due to its instability, I don't think that will occur. With government and central bank-developed instruments that help with regulation and its impact on an economy, fiat currency has shown to be a trustworthy medium of exchange.Nobody knows and examine the potential roles that cryptocurrencies will play.
We do not yet know what would happen to global financial stability if cryptocurrencies were to replace fiat money.
Not only is Bitcoin highly volatile, but bitcoin is not controlled by the government so the possibility of it becoming the world currency is unlikely. The government will never accept something out of control. If we are the government and there is something that threatens our power, we will also seek to destroy it rather than accept it.