changing IP is not really enough for privacy, there is many ways to fingerprint your machine/browser and uniquely identify you across networks

https://creepjs.org/checker

No, but it's the obvious starting point. You can then put additional laws on top banning fingerprinting out of band (if you care about window dressing), fund development of anti-fingerprinting technologies, fund Tor, run exit nodes in a transparent and publicly auditable fashion, etc.

It's not hard to make privacy work when you are the government rather than working against a hostile one.