Someone who is assaulted or robbed might also benefit from the sense of closure they would receive knowing that the perpetrator had died. Similarly someone who found their partner cheating on them with a rival might find it easier to move on from that if their rival was then killed.

In general I don't think that society is best served by legitimising and implementing the irrational desires we have for killing people who have emotionally hurt us.

I think it would instead make sense to try to improve the support given to people who have suffered from crimes. If this means years of expensive therapy, paid for by the near-slavery of the perpetrator carrying out their life sentence, then we could have an outcome that is slightly more humane.