If that is its purpose it's been remarkably unsuccessful.
I'm not claiming that government is the only form of unjustified authority in our society. Such structures exist at all levels from the household to the entire world. I think people should recognize both the unhelpfulness of these structures, the unjustness of them, and start working against them. So yes there will probably always been differences of power between people, but we should always be working to eliminate those, and work to fight against those who would use their physical strength or whatever to impose power over someone else. Murder is probably always going to take place, but that doesn't mean we should work against it.
Lack of unjustified* authority.
So we should do some sort of... policing? I'm sorry, I fail to see why your power structure would be any better than the one it is replacing. Whenever someone has power over someone else, that power may be abused. And someone will always have power over someone else. When you fight against those "who would impose power over someone else", you are imposing power over them.
Which is itself an exercise in enshrining an inequality in power.
Yes, but I fail to see why the alternatives would be any better. As I said, there will always be an inequality in power. I don't know about you but despite all of their shortcomings, I prefer my local police department to unorganized militias or tribal councils.