So your principle reason for the death penalty is vengeance as the case for deterrence isn't found in the criminological literature?
1. The moral case is sound for eliminating it unless you vengenance. The small number of cases makes an economic argument not equal to the moral one.If the moral dilemma against the death penalty is we occasionally put an innocent person to death - then we should eliminate the death penalty. We should also continuously re-try cases for all people serving prison sentences. We have reasonable doubt as a standard for a reason, because humans inherently make mistakes.
2. We don't continually retry. That's a silly statement. We re-try when some new circumstance comes to light. I don't see how this follows. There are some horror shows were the person could have been acquitted with DNA evidence. However, the prosecutors argued against an appeal as the time limit for appeals was up, even though it ran out before the technology existed. Luckily, a judge said that was stupid and the person freed.
Emotionally wanting to kill the person is understandable. I would like to parse the motivations - emotional or cognitive.