You state: "Therein lies the problem. How are you, the “officer” to know which category of individual you are dealing with?"
The answer, of course, is easy: when they actually break a law. Which, in the scenario provided, deranged or not, the individual in question hasn't done. If you aren't sure whether someone is a deranged felon or a law abiding citizen, it means they haven't done anything [in your presence or witness, at least] that is either deranged or felonious. If you don't have evidence enough to know that they are for sure a deranged felon, then you, as an officer, are legally required to assume they are a law abiding citizen. As a retired Sergeant, I would assume that you know this.
If you are sick of being 'pawns', the answer to that, too, is simple. Stop knowingly, falsely, and to be frank, feloniously ticketing, arresting, and prosecuting people who haven't broken the law.
In my experience, I've seen less people commit crimes while open carrying a handgun than I have seen commit crimes while open carrying a badge.