It's a valid point you're making, but I would still argue that the death penalty isn't the answer.
I think we need a radical overhaul of our approach to criminal justice, personally. Imprisonment should only be used to protect society from those who pose a significant risk of harm; not as a catch-all for all crime. Those who have committed serious violent crimes, especially multiple, premeditated violent crimes, should be accommodated away from society on a permanent basis. They should still be treated humanely and have their basic human rights respected, but they should not be offered the opportunity to reoffend. Fewer and smaller prisons, with longer sentences for those who really need to be in them. Alternative, community-based responses to white-collar and non-violent crime.
We can protect the innocent from recidivist murderers without resorting to state-sanctioned killing, and that, as a civilised society, is what we should be doing.