Privacy-conscious apps and communications tools need to be developed, and we need to build the consensus that privacy is important.
(Feels like we have this same discussion over and over on HN.)
Once that's the case, otherwise legal activities (e.g. protesting, or making political statements) run the risk of making you a target. Law enforcement can then punish you for your legal activity by selectively enforcing this other law.
The resulting situation is one where everyone knows to some extent "you better shut up if you know what's good for you", and puts a chilling effect on otherwise legal forms of civic engagement.
You might point out that there are already laws on the books that let them do this, but I'm sure they wouldn't mind another.
Governments will sanction the major proprietary OSes and compel Apple, Google, Microsoft to participate in their surveillance programs, and those will have remote integrity attestation and will be the only hardware and software you will be able to use to access essential services and the internet as whole, most likely.
The usage of alternative software won't be outright illegal, but will get you on a watchlist. Like you said, they don't need to make other software illegal, just make circumventing the blocks illegal.
They can't arrest everyone, but, it's one more gray area thing that can and will be used against you should the government ever decide they have a bone to pick with you specifically so you can get away with it for a long time, until suddenly you don't.
If you're in a repressive state and you're worried about your data being exfiltrated the best security practice of all is not to create records of illegal activity. If you have to store such material, don't keep it on a communications device, put it on an external storage device, hide it somewhere outside your home, and don't tell anyone about it.
Is there really no way we can make it technologically impossible for them to exfiltrate user data?