There are two giant flaws in this line of reasoning (if indeed, the question is rhetorical).The death penalty does not work as a deterrent, so why should lesser punishments work?
1. If at all, we only know that the death penalty as an alternative to life imprisonment, does not serve as a deterrent. There has been no study, to my knowledge that has compared the death penalty with the alternative option of walking scot-free. I highly doubt you'd find the same result, were such a study conducted in a fantasy land where a murderer or rapist would not be incarcerated for his/her actions.
2. The second flaw is in the implicit assumption that deterrence of crime depends only on the nature of the punishment and is independent of the nature of crime. If there was a life sentence for jay walking, I think you find fewer jay walkers on the street.