If someone did horrible, unspeakable things to a loved one of mine and the police caught them before I did, I would want them killed. I understand that not everyone thinks that way, but there are plenty of people in my region of the country who do.
If that's the main justification, they're implying a feeling of closure is worth a small but significant pile of innocent bodies. A potential example of this was just in the news today (see Ledell Lee).
Since the victim’s families have said as much. If my daughter is killed, I would want the killer killed. It would go a long way towards closure.