They will spend a greater amount of resources investigating how to control it via the protocol, then via the userbase, then via incentivized alternatives. We see that kind of thing being looked at already.
I think, in the end, they will conclude they can't control it well enough that way. Best they could do is make it unattractive to most people in places where they can offer a better alternative. In places where the gov surveillance isn't worrying people much.
At that point, they might try more overt methods. Banning, regulating out of existence, jail sentences.
This could become quite extreme, since it does indeed threaten their golden goose.
I doubt if this could be made to happen in every single country though. Still, I'd rather not have my bitcoin and my if linked at that time. Long before this time, bitcoin will evolve to avoid their actions, but people will still take damage.
Eventually, I think they will fail to control it everywhere, but it could become hard to use. What's left then will be interesting to see.