This is exactly where the 2nd amendment and the Blue Lives Matter movements collide. If both civilians and police have the legal right to arm and defend themselves with lethal force, and neither has a responsibility to show restraint or demonstrate cause, then you have created a situation where an innocent civilian and a good cop could kill each other in self defense and neither would have done anything wrong.

Edit: I'm not going to respond to each comment saying there are no good cops. My point is that the cop does not have to be a bad cop for the civilian to have reasonable fear for their life, nor does the civilian need to be a criminal for the cop to have a reasonable fear for their life. Both are legally justified in killing the other person, and both are legally entitled to own a weapon capable of killing the other. That's not a society, that's a war. Ir we didn't already have a police force, and you described their function in their current state to a peaceful society, they would think you were mad.