Here is what I immediately thought when I saw the title of this thread: Everyone here on this board is a martial artist of some sort. What are we all taught in regards to self defence? That you have no ethical or legal right to kill someone unless they are using lethal force against you. Now, once the death penalty candidate is captured, he is no longer a threat. He is isolated from society, surrounded only by the people who gaurd him. At that point, killing him surves no purpose to the the public.
Except when he is released 10 years into his sentence after having served 10 years with OTHER criminals, learning to do things more efficiently. And probably going back to his previous behavior.