It's like: "We'll kill the killers the right way ('humanely', with due process, etc.) so you don't go vigilante and murder them yourselves."
From this angle, assuming no other considerations, the legitimacy of the court system hinges on how often we see revenge killings. One could argue that the U.S. is more civilized now, so discouraging revenge killing is a fairly minor consideration.
Revenge killings are irrelevant. Nobody is saying instead of death penalty we should just free them. They'd be in prison. And if after 30 years someone gets parole, I highly doubt anyone will notice.
From this angle, assuming no other considerations, the legitimacy of the court system hinges on how often we see revenge killings. One could argue that the U.S. is more civilized now, so discouraging revenge killing is a fairly minor consideration.