Technically, governments can ban the Bitcoin-related activities such as exchanging it against fiat currencies but practically it is impossible to do that in my opinion. In worst case scenario, the governments will try to monitor the transaction history of users by accessing a database of the domestic exchanges to determine the tax liability but I do see a rare chance of levying the complete restriction as I mentioned earlier.
The government has full power and they can do whatever they want. the government now considers Bitcoin a threat because the very fast price movement of bitcoins could disrupt the stability of the economy in their country. So the public should be able to play an active role to be able to socialize Bitcoin and never use Bitcoin to conduct illegal deeds because it can make integrity and trust in Bitcoin is increasing.
As many have feared, it seems that one of the main reasons the government has banned Bitcoin because of its nature can be a currency tool for trading illegal activities.
This is a fact and indeed, bitcoin has become the main payment tool in use in darkweb for the purchase of illicit goods such as drugs, hijacking tools, etc.
While on the other hand, the government can not monitor much less get access from every bitcoin account, because the purpose of created bitcoin is as freedom in owning independent bank without the intervention of the bank.