its cheap to execute them, which is what should be done
YES. Save money, save innocent lives, zero recidivism.
Anyone already incarcerated for any crime of violence against a person who is convicted for a third needs the gallows.
They will be a constant threat to other inmates or any other person for the rest of their lives and there's no reason for the rest of us to put up with it. And the death penalty would be a real deterrent if and only if it were swiftly and often applied. Right now most condemned seemed to die of age related illness decades after conviction.