The pact the government has with people is that the government metes out justice so that people don't try to get it themselves. Some measure of retribution, it doesn't need to be the death penalty, works towards this goal. If people believe the courts will punish a criminal they are less likely to do it themselves, it reduces the risk of vigilante justice. That's a good thing because vigilantes are less discerning about getting the right person and considering extenuating evidence. It's a compromise.
Imagine the government found a way to cure psychopathy with a pill. They catch a serial killer who brutally murdered dozens of people, utterly rehabilitate him with their pill and release him the same day. This might satisfy you and some of the other wise and enlightened commenters in this thread, but many people would not be satisfied with it and people would be more inclined to kill murderers in retribution, since the government no longer punishes them.