A really good post, EEE.  I think you are getting at a kind of "emotional intelligence" coupled with the ability to be calm under fire.  Although police forces need people tough enough to handle themselves, I don't think they need people with a "military" type of personality.  It's not the same job, and it doesn't require the same skills.  In that video of the officer from Virginia talking down to the "in-fatigues Lieutenant," his emotional read on the situation was just so obviously bad.  He had a chance to talk to the guy, and the guy wasn't being combative at all.  Why escalate and adopt a command-and-order attitude in that circumstance?  

I know the FBI targets particular personality types for its field agent roles.  And at the risk of running afoul of equal-opportunity employment laws, I think police ought to adopt the same approach.  In short, it (like the NFL or the NBA) should not really be an equal opportunity workplace.  No, I'm not talking about race or male/female.  I'm talking about very particular skills for the job.