I begin with the proposition that there are no absolutes except subjective existence. Everything is reducible and exchangeable except for the subjective qualitative experience of living — for humans most of all, but for plants and animals as well. This proposition is related to the Kantian maxim that humans should always be treated as ends-in-themselves, never as means to some other end.
From the infinite, irreducible, unexchangable nature of human existence, we see an insidious effect of the death penalty being levied for murder — a subtle suggestion that human life is, at the margins, even if imperfectly, exchangeable. That in some way the offering up of the villain’s life in some way compensates the universe for the loss of the victim’s. From a purely economic perspective, we know this is wrong. Two deaths do not equal one life. Though in a reversal of logic, perhaps we are merely reifing a new equation of murder — that the murder takes two lives. In terms of net morality, this is probably correct.
Still, we speak of justice, and we speak of capital punishment being justice — but it is not. Thus the common refrain — it won’t bring back my daughter. Rather, murder is the crime from which there can be no restitution. To attempt such restitution, through execution or through wergild, is to deny the ultimate and unredeemable loss society has faced.
Better than not to kill killers, but rather aknowledge the societal loss and the limits of justice — that with murder, the debt cannot ever be repaid, that human life is precious and unique and when it is gone, it is gone forever.