The point is that they are not a thing unto themselves, they are people hired by the commons to do a job. They have the same rights and responsibilities, they go in front of a civilian judge if they fuck up. Also, as a rule, non-civilians are not permitted to police civilians, at least here. Being a civilian BTW is, and should be, a higher status than not being one, not a way to say "not part of the cool in-group".

Airline crews are also in a respected and trusted role and operate machinery that can cause the deaths of hundreds to thousands of people. They even have ranks and stuff. I've never heard anyone say airline crews are not civilians.

I consider police to be a respected and trusted

I hate to assume, but you must be a white man, and if you're not you're really fucking lucky and should read up a little more about how the police actually conduct themselves and what obligation they have to you (hint: none).