Although this line of reasoning rightly values victims' feelings, the death penalty does not necessarily alleviate their pain. On the contrary, seeking the death penalty is a long and stressful process. It often worsens the pain of victims and their families, reigniting their grief and interrupting their healing process. According to a University of Minnesota study, only 2.5% of co-victims reported finding increased closure because of the death penalty. The study also found that co-victims achieve greater physical and mental health after seeking life in prison sentences, not the death penalty. 
The death penalty also creates more victims- the family and friends of executed prisoners. Like the original victim's family, they must mourn the unnatural death of a loved one.
In an attempt to soothe one family's pain, the death penalty creates an entirely new group of people who must resolve feelings of pain and grief. The death penalty is an ineffective solution for victims and their families. It does not alleviate grief, it simply gives grief to other people.