Your naive nihilism is always astonishing. There are 265 million people in the U.S., of course there is going to be crime. Yet, when governments warn their people about the dangers of visiting certain countries... one has to look at the root of what's going on there. Out of the top ten countries with the highest murder rates... five of them are South American (Honduras, Colombia, El Salvador, Venezuela, and Bolivia). I'm pretty sure a great deal of those countries have also abolished the death penalty. I mean, it's nice to know that someone can go rape and kill a little girl and get to live a full life... especially after they denied the right to live to someone else.
It is a deterrent. China has billions of people... and they practice the death penalty and even their murder rate isn't has high has some Latin American countries.
So, if someone raped and killed your daughter... you be content with him just sitting in prison. You would find closure in that. Call me crazy... but if someone did that to my child... I would probably want to kill the guy myself.