I'd say that's part initial screening, part training, and part willingness to fire people that turn out to be unsuitable. All of that is helped by having access to a broader candidate pool, such as by not imposing arbitrary education requirements.

Something related that's often discussed in law enforcement and military is the idea of being able to hire directly into some upper specialist positions without the person having to rise through the ranks. This is sort of the opposite, admitting that some senior positions do not need an arbitrary field experience requirement. In both cases, it's about better matching the requirements and subsequent training and career progression to what's actually needed for the job. This kind of rationalization is the upside of a tight labor market.

I don't need police to have a 4-year degree (or a 2-year degree), but I would like them to be highly educated and trained.

Have you ever had interactions with police? Did you find them psychologically balanced?

The answer to this may vary heavily by country, local jurisdiction, and certain demographic characteristics of the person interacting with police.

Systematically, I think the answer is no. Whether or not this is a encouraging or discouraging answer depends on the extent to which you expect systems to solve human problems.