There's ample evidence that this is already happening, eg. recent headlines about kids being radicalized at increasingly younger ages, groups like No Lives Matter that embrace violent nihilism, increased domestic terrorism, record high gun ownership across both sides of the political spectrum, authority figures that just do whatever they want and ignore any form of law or accountability, etc.
We're already at a place where most people don't care what other people think of them.
Issue is, as long as the government has the big guns, what the government thinks of you will still matter in a major way.
In such an environment, most people are going to choose to have some kind of way to prove to the government what they did and what they didn't do. Not because they care what other people think as you're implying, but rather because they very much care that the government not get the wrong idea about them. Because the government getting the wrong idea about you can be fatal.
I suspect that we're saying the same thing but with reversed causality. Both of us agree that non-deterministic enforcement breaks down the incentives needed for pro-social behavior. You're saying that this will cause people to demand ways to improve the governments enforcement abilities. I'm saying that this will cause people to adapt their behavior to the new, lessened enforcement abilities. In defense of my point, I'd point out that changes to government are a coordination problem while adaptation of behavior is an individual-only response, and it is much easier to effect changes to your own behavior than it is to convince 300 million people to agree on a solution and implement it, particularly when the root problem is a lack of enforcement ability.
The government coming up with one way to track everyone is not really necessary to get people to submit to tracking. In fact, most of the law enforcement "watcher" types wouldn't want that anyway. Not only is having a myriad number of ways to track and surveil people is far preferable to law enforcement, but it also allows people to individually choose to set up all the Ring doorbells and security cameras and GPS trackers and smart glasses based body cams etc etc all on their own.
And they'll happily choose to buy all that stuff voluntarily and without regard to what everyone else is doing.
Imagine that the populace supports widespread surveillance techniques, and so cameras are setup everywhere. Some hacker group figures out how to hack into the cameras and insert deepfakes in them. Now members of that hacker group have a government-proof alibi whenever they want it, and can commit crimes at will, and get it blamed on others. Justice goes out the window.
This is how the "watcher" types are trained. Information is only valid if they can get it from multiple independent sources. So they love when new tracking and surveillance channels are released. (Social media apps, or smart glasses, or doorbell cameras or what have you.)
The bar would be much higher than compromising a single channel. With multiplying channels, the task of compromising them all approaches impossibility.