The government is phasing out cash, as I covered in my prior post.
Now whether anonymity will work reliably and whether the coin can't be shutdown by filtering at the routers controlled by the major governments is technical discussion that will have to wait until the details of such a coin are known.
It will have to be very technically robust to survive. Government will be looking for scapegoats to blame the debt collapse on.
Anonymous cryptocurrency is sure to be a target.
Many people in government are going to be looking for a place to hide their ill-gotten wealth from the 99% as they take it from the 1%. They might just like to have a haven too. (sorry there are no absolutes, no perfection)
They will still be able to get all those people who mess up and don't report transactions and wealth that can't be anonymous. And I think they will be much busier hunting down all the Bitcoin millionaires who cashed out. That will rather easier to do than blocking all internet traffic of a certain type in every country in the world (I don't think they can do this yet, although maybe I am naive).
I think they will find much lower hanging fruit, but again some of that determination is in the technical details.
Anonymity is the not the main or single feature I want to see in an altcoin.