To the semi rational law abiding mind, the death penalty is the ultimate deterrent.
But the flaw in that reasoning is in assuming violent criminals are rational. And sit there with calculators and play expected gain and against possible losses calculations. And then conclude, if a penalty is high enough, no expected gain is great enough to risk the death penalty.
After all, Psychological study after study has concluded the death penalty is not a deterrent to such crimes. Especially when many violent and senseless murders are committed for miniscule economic gain.
After the fact of a murder, and convicting the the one to blame in a court of law, society is face with three slippery slope problems. (1) We can maybe all agree, get such people off the street, put them in iron cages, because its not safe for the rest of us to have them still running around loose.(2) After that, it gets down to costs, especially with the legal system of the USA. And the fact is and remains, its always cheaper to jail them for life even after housing and feeding is factored in, rather than to try to seek the death penalty. (3) Then we have another factor, our legal system does not always work, and we find we killed the wrong man of woman after they are dead---when new evidence comes in.
Then there is another factor not often considered, because of a defect in prosecution funding. Most murders are State offensives, which means the county in the State where the murder was committed has to bear all the expense of the trial. And since nearly every county in every state has minimal funding for its prosecutors and investigators, will soak up their budget for an entire year if they seek a death penalty trial. Meanwhile lesser criminals get a free pass, because there are no resources left in their budget to prosecute them. So they have a field day while their victims get screwed.