I believe it should be enforced only in certain specific cases that pose large scale societal harm. One thing reactionaries always jump to when talking about the death penalty is murderers and rapists, and one can argue how much the harm of those crimes is large-scale or societal, but I think they pose way less threat in the abstract to society than, for example, a pogrom inciter. Specially since those usually get barely any punishment because they "personally didn't kill anybody."

I also see the "punishment" aspect of the death penalty to be completely moot. Even just a life sentence in solitary can be a way more harrowing and punishing experience than however long the death can be extended to, so focusing on the broader social impact of either a deterrent or a "permanent removal from society" is the way to go. This is not a moral stance, though, and different societies with different moral and cultural values will have to take those into account too.