I have seen no evidence that execution actually removes trauma. Trauma stays with people even after the cause of the danger is removed. There might be a sense of "justice" to slightly balance the trauma, but nothing that can fully remove the scars of it.
I stand by my opinion that the point of execution is not for the emotional state of the victims regardless. In a majority of murder cases, you could execute a scapegoat and get the same effect so long as it appears that you have the right guy.
In the few cases that we are 100% sure we know who did it and the crime was extra obscene, I can look the other way for a death penalty... but I still think it's a slippery slope because it takes us away from the purpose of the justice system.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside