> What about justice for the society in which the crime took place?
This for me is one of the strongest arguments against the death penalty. If the state can kill its prisoners and the state's government falls into authoritarian hands, one political faction, the authoritarian faction, can simply kill off those who oppose it. Did the accused commit a crime, a "crime", or do nothing at all? Well, too late to find out.
Of course, an authoritarian government can bring back the death penalty, but at least make it harder for them to hide what they are doing. And the longer your nation goes without the death penalty, the more egregious it is when the authoritarians reinstitute it, the more obvious it is what they're doing.