Bitcoin is intended to serve another purpose: To demonstrate the behavior of a money system that is not controlled by a government.
As with any technology, people use money if it's useful to them. If a country has a poorly managed money system, then people start to use the money of some other country, or barter. If bitcoin has a chance of supplanting government money, it will happen when bitcoin works better for the people using it. I suppose this could happen sooner in countries that have really bad money, or if the use of government money becomes prohibitive because of transaction fees.