Isn't that sort of what a "state" is? In the absence of a state, individual humans would occasionally have to end the lives of other humans, but if one exists it will jealously guard that prerogative for itself.
Are you saying a "state" is just something that jealously guards prerogatives for itself (love that line btw)?
I agree occasionally humans do have to kill other humans because I'm not a pacifist but I think the death penalty isn't to stop a horrible act, because the person is already caught, but to punish.
Various states jealously guard various prerogatives, but the ur-prerogative is violence. The subjects of states without violence will eventually just live how they want to live. The whole point of states was to prevent that.