Quite simply, if you had to pass a psych exam to be in EMS, we'd loose half our personnel the next day. We are all a bunch of loonies that enjoy this kind of work, and without the crazy we'd never get people to willing subject themselves to such long hours of blood, guts, vomit, and under-appreciation.
Seriously, though, I think it has to do with the nature of the job combined with EMS's relative infancy as a profession.
Nature of the job: Police work is a job that centers around authority over strangers. The use of force is necessary at times, unfortunate as it is. Deadly force is discouraged but authorized as necessary. In order to do this job, you have to make sure that the person behind it is getting in for the right reasons. That you aren't a sociopathic bully out to do nothing but abuse everyone within your reach.
EMS, however, is a job where we don't exert much authority OVER a person. Yes, there are times were we "take custody" of a patient, if they are not competent or if they are arrested under a police officers authority. Under normal circumstances, if the patient doesn't want to go, we can't make them. I had a woman crack a windshield with her head the other week, and didn't want to go to the ER because she had no insurance. I tried to convince her, but she wouldn't go, and I couldn't make her.
If we DO overstep our bounds, there is no debate. If I were to have tied that woman to the stretcher to take her in for her own good, I would have lost all my certifications, which would have been the least of my worries as I sat in jail for kidnapping. I overstepped, wham-bam, you're wrong and you're done. The worst we can do as EMT/Medics is abuse our right to strip and/or touch our patient by using it as a sexual device. Either voyeuristicly and unnecessarily stripping down a patient for an "exam" or touching areas you shouldn't be for a little longer than we should be, for instance. And accordingly, our backgrounds are scrubbed by almost any agency to make sure we have no sexually related criminal charges in our histories. I don't know about you, but my background check went back to when I was a teenager to make sure there wasn't criminal sexual assault charges or suspicions all the way back to my high school.
In short, it's a job that nobody is going to get into without wanting to help people, barring the sexual deviants who would get off on an unconscious person. Police work is a job with a lot of authority which could be and is at times easily abused and explained away just as easily by a lie or twisting of the truth. Much more attractive to nutjobs who want a good, "legal" way to exert power over people.
Infancy of our profession: Let's face it, we are fairly new. It has only been, what, since the 60's or 70's that we've become a real service? Before that, it was just 17 year old ambulance jockeys yanking kids off the battlefield and running them back to a med station hopefully soon enough to cut a limb off and save a life. We don't get as much respect as we'd like and in a lot of cases deserve from the rest of the medical community, which has existed in various but mostly familiar forms for hundreds of years now. Doctors, nurses, surgeons... they all have a long and storied history.
Medics? EMTs? Not so much. We have a couple of decades to hang our hats on, and for much of that history people were given no formal training beyond how to put on turnout gear and turn on the lights and siren. And in that short existence, we have seen our continued absorption into other agencies like fire or contracted out to medical transport companies. We are still trying to find our own place on the medical map, as much as we may think we have it figured out. We still don't have a real national educational standard to what should be considered a medic or EMT, and we are continually struggling to get people to consider us more than "ambulance drivers."
If we ourselves are having trouble being able to define what is necessary to be a medic, it's not surprising that we are also having trouble deciding what should be used to disqualify you from the job. Yeah, we have a couple easy, obvious ones like being a sexual predator, but that pretty much goes for any ol' job that requires you to work with people let alone undress and touch them. We need to grow as a field a bit more before we will be able to settle on what weeding-out processes should be used to separate the wheat from the chaff.