Not sure civilian cops would understand the military culture well enough to be effective.
The typical MP is,in MY experience either a young kid who enlisted and sent to MP school because he was big and strong,or a lifer thug that likes being a MP because it allows him to screw with and bully real soldiers.
The smart ones that re-elist and stay in law enforcement,become army CID investigators who wear plain clothes and investigate real crimes like real cops.
Seems to ME that most of the kids who join and then become MP's,re-enlist for another career field if they re-enlist.
I have been out of the US Army since 1970,and to this very day when I see a MP,I want to hurt him and my first instinct is to look around to see if there are any witnesses close enough to recognize me in court.
I once had two of them in uniform trapped in a mens room in a local bar where they had jammed the door shut for about an hour to keep me away as the bar owner gave me free drinks and talked me into going away and leaving them alone. This was maybe 2 years AFTER I got out of the army.
BTW,if it matters,they were both from the leg MP unit at Ft.Bragg that makes their careers out of arresting SF soldiers on bogus charges to try to destroy their careers. It was MP's from this unit that arrested me on a Friday afternoon about a week before I got out of the army,arrested me,and took me to the drunk tank at the Fayetteville PD for the"crime" of stopping at a 7-11 off-base for a gallon of milk while still wearing fatigues on the way home from duty. I only lived about a block from the 7-11.
Yes,I know. Today you can legally wear fatigues anywhere,but back then you had to be wearing a dress uniform if you were to go anywhere off-base other than home,and you were not allowed to make any stops on the way home.
They both seemed to think this was funny,and laughed about it all the way to the Fayetteville lockup. One even tried to tell me "I COULD have been Special Forces if I wanted,but I quit jump school after 4 jumps because I didn't want to be one of you phony bastards." He knew so little about SF that he thought graduating jump school meant you were going SF,so he lied about even going to jump school. The whole ride into town I kept repeating to myself,"You only have less than a week left in the arm,keep your cool,keep your cool!"
Had to call my CO to bail me out of jail,and then had to go to the impound yard and pay to get my car released because they had it towed off when they arrested me. The CO wasn't even pissed at me for interrupting his Friday night. This kind of crap happened so often he was used to it.
I guess it would be safe to say that I don't much like MP's.
