It is very difficult to just assume Bitcoin replacing fiat money. Even if it does,it will be a process of slow adoption that will take decades. This is because the Government in general has to take careful and necessary procedures and/or regulations that will ensure a safe transition from Fiat to Bitcoin.
Perhaps the biggest challenge is the volatility of Bitcoin and Altcoin. Most currencies at least of developed countries are regulated by their respective Governments and allowed to "float freely" a.k.a Government intervention if required.

Other issues that will complicate such process is international trade.