It's simply impossible for Bitcoin to completely cut al ties with governments, but that shouldn't be the main point. Important is that Bitcoin gives us the ability to store a portion of our wealth outside the banking system if we so wish. It doesn't mean we must do it, it's just that we have that option open to experience some level of financial freedom. I am sure that a lot people find it scary to be responsible for their money as Bitcoin allows them to do so. That's why the majority of the people will choose to continue with storing money in banks. They can't handle that level of responsibility themselves.
That's why accepting Bitcoin by governments is important
At least, in the same degree as foreign currencies are accepted in most countries, up to a point where you can open a deposit account in any major currency, e.g. the US dollar or Euro. If Bitcoin is officially equaled to a foreign currency and there are no specific regulations prohibiting banks from dealing with Bitcoin (like it is done in China), regular banks would be able to open Bitcoin accounts in pretty much the same manner they do it right now with foreign currencies. Thereby people which are scared to be their own banks would be able to use Bitcoin just like they use foreign currencies today. This doesn't in the least mean that anyone will be forced to use these services as I already anticipate plenty of ado rising against this possibility