My take is pretty simple; Outside of wartime conditions there is rarely if ever a situation where resources are stretched so thin the state can't afford to incarcerate someone indefinitely. If you kill an innocent person that's it, they're dead. No going back. If you lock up an innocent person there's still a chance that the truth will come out and they'll be freed. For the most part the death penalty is about revenge and doesn't serve any legitimate social interest. We know from extensive research that deterrence doesn't work. Additionally, hope for mercy can be used very effectively to turn criminals against each other, induce spies to give up useful information, and so forth. Mercy is a very powerful weapon. People will resolutely face death, but it's a lot harder to keep your mouth shut when you've been treated humanely and with respect by your jailers.

Generally speaking, and excepting wartime exigencies that might demand more immediate and decisive action, I don't think it's ever in society's best interest to execute people.

And, of course, ultimately, the goal is the abolition of carceral punishment entirely, and with it the cultural and economic situation that makes the kind of violence we're dealing with endemic.