The death penalty is now a painless injection that does not cause pain to the person be executed. It is a way to show criminals what will come of their cruel actions. Never being able to see you family again is a wake up call to those who are given the penalty. The last thing they know is being strapped to a chair, and then painlessly dying.
The cruel and unusual punishment is not the way or how painless the person dies, it is that they know they are going to die. To know that they are going to die is torture and if the persons are dead there is no lesson to be learned so them thinking of never seeing their families is irrelevant. Also there executions are not public so no lesson will be learned by other possible murderers. In some cases innocent people are sentenced to death and it is latter discovered because of newly discovered evidence. An example is the Todd Wilingham case. In some places the death penalty can be abused and used to discriminate. One in every ten people sentenced to death are mentally ill.
If it is torture to know you are going to die then wouldn't that make others not want to go through the process? If they can't be with family when they die it is relevant because they will knowingly wait for death without at first seeing the people they love. The executions may not be public, but just knowing the loneliness involved in the process will create a second thought. The executions don't have to be public just announcing the journey involved will be enough to make people not want to suffer through the process.
As stated earlier based on studies the death penalty does not deter crime. Also time in prison has no down side. It is cheaper the appeals process for the death penalty costs millions of dollars. The appeals process makes it hard for the victims family to move on and finish the grieving process. Also capital punishment is against most religions. The death penalty is an unnecessary waist and only harms innocent people and the victim's family.