Agreeing with you, I think the reason many people see former military as good candidates to become police – they’re skilled with weapons and squad operations – are NOT the things we want in regular police. On the contrary, much better to have people skilled at resolving things without use of weapons. I’d say ex-military would be very suitable for SWAT but not necessarily for regular police.
I’ve seen it said (weasel words meaning “I can’t remember who or where”) that people coming out of the army are very good with disciplined weapons-handling and following rules of engagement. That’s good, minimize accidental shootings. Again, only useful for encounters with weapons involved. (And the current rules of engagement – “I feared for my safety” – should be revised to something like “there was no possible way, not even running away and coming back later, to avoid using a weapon”.)
From Lt. Col. Dave Grossman’s On Killing (other people here have mentioned it too), we know that part of basic army training is overcoming people’s natural instinct to take care of each other and teaching them to kill instead*. That’s not a strong recommendation for policing based on deescalation and connection. I don’t want to overgeneralize because I expect a lot of ex-military do fine as police, but it still seems like it contributes to the problems of weaponized policing rather than fixing them.
(*And we do ask a lot of them. For many, they keep paying the price long after leaving the military.)
ETA: This looks to be Grossman’s book as a PDF (virus-scan appropriately): http://kropfpolisci.com/cognitive.grossman.pdf
