Usually these systemic problems with incompetence and abuse of power are personnel problems, that stem from having a limited pool of people willing to do a hard job, and covering up for their mistakes.
So they inevitably end up being unqualified, not very intelligent, wanting to do it for the wrong reasons, and feeling a sense of invincibility from the lack of accountability.
IMO the solution is to pay better and invest more in better training. That way you end up with more intelligent people, that are willing to do the job, and they're better trained. So I totally agree with your last point here.
They need to be highly qualified, because a lot rides on their awareness, and decision making ability. Not just the hockey version of power hungry mall cops, that let the stores get robbed, because they're harassing skateboarders or something.