It is true that they are civilians, but they have been given both special authority and much, much more responsibility than are other citizens.
A great example is that police are obligated to at least try and arrest those committing major violent felonies. But under generous rules, in many situations, ordinary citizens can just kill them.
Police are burdened with paperwork, redundant supervision and review of their actions, and need protection from their superiors with a union. But that is the price demanded of them by a distrustful public.
On a lighter side, when I worked for the PD, we had an officer who actually wrote himself a speeding ticket.