When everyone uses cryptocurrency to trade, the government will not get any benefit, the tax can't be collected, and the government will go bankrupt because of the cryptocurrency. So the government will definitely cooperate with the cryptocurrency.
And how exactly are you planning that governments cooperate with cryptocurrencies? The developers of bitcoin are never going to introduce any kind of code that will allow the government to tax you directly, so governments will need to try to find a way to identify the people that are using bitcoin or any other cryptocurrency and even if they find a way to do that, we still have anonymous coins impossible to track.