Well, banks would still take from people as much as they can. They will force governments to regulate btc, this would make the currency just another asset they can control. End of story.
There is a difference between controlling the usage of a currency and then controlling the currency itself, so your story will not play out. Bitcoin remains a decentralized currency until otherwise, and then the highest the government can do is to regulate the exchanges. This does not give them control over the currency, nor does it give them control of P2P exchanges as there is no way they can ever do that. Worst that would also happen is for them to create their own cryptocurrency which they can control, but they cannot impose it on the citizens.