An advantage of having a death penalty,

....even if it is not often used, is that defendants can and will modify their behavior to avoid it.  A recent example is "Dr." Kermit Gosnell, who gave up his right to an appeal in exchange for getting life in prison without the possibility of parole.  He will die in prison, as he should, and the taxpayers will be spared the expense of appeals.

It's worth noting as well that if Gosnell changed his behavior to avoid the death penalty--though of course sadly too late for his victims--then we'd be silly to argue that the death penalty can not function as a deterrent.  It's also worth noting that the deterrent effect depends strongly on whether the penalty is administered justly, as anyone from Illinois can tell you.

(there, I'd limit it to politicians, of course)