Yes it is. But a reason used for CP is the personal benefit to the families of the victim. That's my argument about forgiveness comes in.
The state exists to do justice on our behalf, and part of that is vengeance.
Well, vengeance has been shown to not be very helpful. The state should not be in business of vengeance but PROTECTION of our lives and freedoms from any source including criminals. So secure incarceration for that reason, IMO, is a valid function of the state.
The state’s role is punishment for crimes. Vengeance, protection, rehabilitation, etc are only the excuses used by society to justify punishment.
Up above, you commented that vengeance felt good for a while, but that ultimately, only forgiveness would soothe the victims' families.
Since vengeance does therefore seem to be of some benefit, the murder victims' loved ones would be best served by first seeing the killers executed, then forgiving them in time.
Self-protection is our individual responsibility. But private vengeance, or vigilantism, can be problematic. That’s where the state comes in.