For now bitcoin replacing money is impossible. It is also impossible in the near future since banks and governments will take actions to stop bitcoin for replacing fiat. In the far future, it might be possible that bitcoin replaces fiat if and only the government officials or leaders at that time supports bitcoin and will allow it to be used as a currency. There's a low probability of it happening but at least there's a little chance that it might happen. 
i think it is not impossible as anything can be possible so bitcoin can replace fiat but it will take a lot of time, and the second is that band and government cannot stop bitcoin from increasing its value and becoming more and more popular as the price of bitcoin, as bitcoin is anonymous and now one know that who i using it and from where.