Personally, I lean more towards the idea that the criminal justice system's primary purpose should be to rehabilitate criminals; seeing as death precludes that from ever happening, in this world at least, it's not a form of punishment I could ever see myself supporting.
The whole hoopla about rehabilitating criminals is a kind of particular type of idealism rather than something based in facts and reason.
Rehabilitation is an ideal, one somewhat tied to left wing ones, not some universal cure to criminal problems. It's one of limited utility, even if it does have some, and it is more effective in some scenarios than others.
We know there are criminals who will never be "rehabilitated", even if you would put the most renowned social scientists on their case.
We know there are criminals who don't need to be "rehabilitated" yet need to stick around in prison to be an example for the greater society.
We know many criminals in prison will, for all practical purposes, get socialized into worse habits and views that they came in there with due to interaction with other criminals, who aren't nice or highly cultured people on average.
Some non-considerable part of the successful cases of "rehabilitation" are merely cases of an older and simpler mechanism - people who went to prison, didn't like it there, and don't want to risk being there again.
In practical terms, the main point of prison is keeping in people who would prey on the general society in criminal ways if they were free to be in it, while the inconvenience of being stuck in prison is also a punishment in the simplest and most traditional sense of the term.
Besides; even if he never does, so long as he also never has the opportunity to hurt anyone else ever again either way, the only thing The Death Penalty would accomplish is saving a few bucks that would have otherwise gone to keeping that bastard alive, which usually ends up getting canceled out (or even exceeded, especially when they're successful as in this case) by costs associated with allowing appeal after appeal when such a sentence is levied.
That's more of a legal system cost problem than an inherent death penalty problem - a bullet costs much less than a dollar after all. Consider that keeping the bastard alive costs not so "few" bucks at all - usually more than the average working class person earns in the same year and place. In cases of more troublesome, dangerous prisoners, or prisoners with major health problems, more than a middle class person.