This raises the question of whether the parole boards and other political characters make this impossible.
Very good point.
That's the position that I would take. It's a public safety issue above all. In the Summa Theologica, Aquinas justifies killing in self-defense under the principal of double-effect. The primary purpose of the act of self-defense is a good (preservation of one's life) while the killing of the assailant would be a simultaneous evil effect.
Capital punishment extends this principle to society as a whole. The primary object of the State's act of executing a murderer is the defense of the lives of its citizens. The simultaneous evil is the killing of the murderer.