Never heard that one either. I don't think that's a known reason in criminal law for capital punishment, but I think it's imaginative and creative. But it fails because the same facilities that keep a dangerous criminal separated from society also keep revenge seekers on the outside from getting to the convict. How these matters are handled within the prison system is a whole other discussion.
It goes back to the middle ages, where private wars, or feuds were frequent. A nobleman, or notable, would hold court and render justice. As the common law caught on, a judge would take over from these manorial courts, and so the power and prestige of the king was behind the decision. IAC, I think that the death penalty should stand in exceptional cases, and for convicts who kill other convicts.