Yeah they're going to try to it, or really just force it on us, regardless of what we do. The people who run our world governments...they already are the monsters, they already are the warlords, they already are the people they told us to fear. They have insulated themselves from the will of the public.
So it's not a matter of "if", it's a matter of "when". Really, we shouldn't be considering what governments demand of us, because they don't consider what we demand of them. We need mass mobilization of the public. And at least on the online front, that's reasonably easy: everyone should be on Tor as much as possible, everyone should be using adblock when forced onto the clearnet, everyone should ditch all FAANG [1] services and be using FOSS federated alternatives as much as possible, and people who provide web services should accept connections from Tor endpoints and people who "look legally sketchy".
[1] Yes I'm aware that a lot of Fediverse sites use AWS in the backend. I think that, at some point, we need to move away from AWS, even if it means significantly downsizing the Fediverse and the rest of the Internet.