Every debate on the death penalty I have seen never presents the key benefit of the death penalty that I am aware of. When I taught forensics I noticed that many of the major discoveries in forensics were made during death penalty cases and in fact the death penalty was the prime motivator for the discovery. This is true of fingerprints and DNA and fiber analysis.
1. Some argue that the Death penalty is more expensive than life in prison, that these cases can take 25 years to finally exhaust all appeals. To me this is the major benefit of the death penalty. The death penalty provides time, resources, and volunteer labor to look for a way to prove innocence. These discoveries benefit thousands of people, not just the one on death row. I would never want the death penalty to be the cheaper alternative. No one wants the judge sentencing a person to death in order to save money.
2. Some argue that the Death penalty is biased. Minorities and the poor are much more likely to get the death penalty. This to me is a very big justification for the death penalty. The bias is for all incarcerated, not simply death penalty. If I was poor and innocent I would definitely want the death penalty. That would open the door to all kinds of non profit services that would help me defend myself. How is life in prison a better option for someone who is innocent? Also, things like fingerprints and DNA have helped to dramatically reduce the number of innocent people in prison from just 100 years ago. Therefore every advancement made in forensics benefits the poor to far greater degree than the rich.
3. Some argue that the death penalty is not a deterrent to crime. I agree, that is not the benefit. The benefit is not that it motivates criminals not to commit a crime, no the benefit is that it motivates researchers and lawyers to prove that an innocent person is innocent. This is undeniable, look at the pro bono work done because it is a "death penalty case". It is obviously a motivator for lawyers and researchers.