Oomis:
While it is true that killing people is the most certain incapacitation, the death penalty is usually advanced on the grounds of retribution. I notice nobody else here is interested in retribution, only deterrent.
Deterrence makes no sense as a sole justification for punishing people.
If you believe that deterrence is enough justification on its own, you would support punishing people as long as we can convince everyone else that they did it, regardless of if they actually did it.
Deterrence only makes any sense with an appreciation for retribution.