When I was an active duty MP Officer, most of my soliders had joined the Army as MP's for the following reasons:
1. They wanted to be hometown cops, deputies or state troopers
2. Most Departments have a min age of 21. (they were 18-19)
3. They could put 4 years of LE experience on their application. (Even though my platoon was direct support to a Mech Infantry brigade and we did maybe 4-6 weeks of Garrison Law Enforcement per year, the rest of the time we were out in the field playing "motorized infantry". But hey, who's counting....)
4. Veterans Preference Points
5. They also took CJ correspondence course and other college classes available on-post. Several got their Associates in CJ and even a few managed to get their Bachelors.
6. They could show that they had already been through a "Police Academy" (MP AIT or OSUT). So they most likely have the mental and physical ability to complete the civilian version.
Compare that to the guy who maybe took CJ classes at ITT or Comunity college or even the guy with a BS in CJ from a "real" University, versus a former MP who during the interview can talk about having done Traffic stops, breaking up Barfights, taking statement, interviewing witnesses, investigating and securing crime scenes, etc. BTDT vs "I read about it in a book/sat through a class on that."
Even Non-MP types understand chain of command, can follow orders, and for the most part think on their feet in periods of extreme crisis/duress. That's why most PD's like hiring ex-military.