Bitcoin is
-censorship resistant (no bad actors, random seizures, totalitarian regime)
-decentralized
-open and borderless (this remains intact)
-neutral (this would get tampered with as now they know who you are, bitcoin does not know or care who you are)
If all you have is the open and borderless thing that remains intact from everything Bitcoin is, it isn't Bitcoin or anything that was thought about at the beginning of all of this.
I'm not much into conspiracy theories, but I think it can theoretically happen. With a digital currency, you get paid with it and transfer it for everything that you pay for. Governments would be able to track every transaction and they will automatically deduct taxes. (I'm sure the tax code will be modified quite a few times by then)
Governments would be able to shut down payments from certain wallets, like if you were under suspicion of a felony and have not turned yourself in. Similar to what Julian Assange experienced when visa/mastercard/paypal donations were cut off.
There are other anonymous digital currencies where one can survive without the Gov backed blockchain that I'm sure will be used extensively.
Just thought it was an interesting topic and thinking off of the top of my head...