I see little to no benefit in the death penalty, and I think the risk of killing an innocent person far outweighs any of those potential gains.
In general, I think it is the completely wrong direction for our prison systems. Prisons should move towards a rehabilitation based system and away from the punishment based system.
What do you mean by rehabilitation system? Like if someone raped and murdered a child then 25 years got out cause he reformed, or practical slave labor in the prison to create things for the outside world (which many prisions already do)?
Basically, a prison system has five goals: retribution, incapacitation, deterrence, restoration, and rehabilitation. The US system focuses almost exclusively on the first three. That means that if someone commits a crime, we want that person locked up for long enough for us to feel like they got what they deserved. However, it also means that when they get out, what they are leaving with is ten, twenty plus years of being locked up with other criminals away from society and often mistreated. That plays a part in why we see such high recidivism rates. Some studies even suggest that prison actually increases the likelihood of committing another crime, not decreases it in the USA.
Other systems, notably the Norwegian system, feel that while punishment is important as a deterrent, the overall goal is to reduce crime and working to help prisoners gain professional and social skills does that more successfully than working to punish them. And it works. Norway has some of the lowest recidivism rates in the world as well as low crime rates and they accomplish this with prisons which are some of the nicest in the world.
As this is a change in whole philosophy, the death sentence largely contradicts these ideals. As such, when you have an individual in Norway like Anders Breivik who killed 77 people, you see sentencing which reflects this change. He received the maximum sentence in Norwegian prisons: 21 years. Not death. Now, that isn't to say he will only do 21 years in prison. In all likelihood, he will never leave. However, this system largely eschews things like "mandatory minimums" in favor of evaluation of whether it is safe for an individual to reenter society.
By shifting to a rehabilitation-based system, I believe we will be able to reduce recidivism rates, reduce crime, reduce the prison population and make sure that those who are likely to commit another crime stay in the system instead of letting them go when we feel that they have been punished enough. That does mean that we as a society need to move away from our ideals of vengeance because while it may feel good for us to say "yeah, let that guy rot", it doesn't actually do us much good. You can see this change in the reaction to the sentencing that Breivik received by the people of Norway and by the families of his victims. There were few complaints from Norway, but a lot from the United States.
I don't think it is possible to move to such a system and influence social mores with the death penalty in place.