It would seem that such a hypothetical level of policing is taking place inside actual prisons, and yet violence and contraband run rampant. If it isn't possible to eliminate crime amongst already incarcerated people, what suggests that an arbitrarily high level of policing would eliminate crime amongst the wider populous? Especially when such levels of policing would almost certainly approach something akin to imprisonment?

The US is already MASSIVELY winning the "percentage of your population in prison" contest. Then you look at the recidivism rates and realise why it doesn't work.

Tough on crime -> more people in prison -> criminals are treated like dogs -> significantly more likely to reoffend upon release, and thus we have a cycle.

No, at a certain level of policing you end up with a police surveillance state, it wouldn't work.