I think you'd need to prove the direction of causality here to be convincing.
> Making policing an easier job would attract less problematic people.
What are "problematic people"? I find this judgment to be very, very troubling. Is it that "problematic people" are becoming police officers? Or that something about the job is causing problematic behaviors in people like you and I?
> Hiring a lot more cops and banning guns would greatly reduce the stress cops are under.
This seems downright preposterous to me. Guns aren't a significant cause of death for cops. Cars (including their own cars) are a far bigger threat. Moreover, there is no evidence to suggest that places where guns are materially banned enjoy less police corruption. Chicago has has some of the most draconian gun laws in the nation for decades and also has a police department indistinguishable from a criminal cartel by most measures.
> The cops in prosperous, egalitarian places are generally pretty chill, so the idea is to recreate those conditions.
Again, I suspect the causality may run in the other direction.
You may be right in the direction of causation that questioned. I look at it this way. Suppose we create a more prosperous, egalitarian society and find out the cops are still jerks. The experiment shows you are correct but at least we'd end up with a better society in other ways. There does not appear to be any harm in performing the experiment.
Even if they carry a loaded gun, they’re less likely to use it against the police than in the USA because punishments are less severe. In the extreme, three strikes laws (https://en.wikipedia.org/wiki/Three-strikes_law) makes even petty thieves with a previous felony conviction more likely to use a gun.
The USA has found a local optimum where cops have reason to be afraid of a large fraction of the population and vice versa, and doesn’t seem to be able to find a way out of it.