If this also serves a deterrent purpose, then well and good.
The deterrent is "if one takes a life, one's life is then forfeit".
You say toe-may-toe, I say toe-mah-toe.
. Granted, if there is a deterrent effect, so much the better.
A subtle difference. But a an important difference.
Libs are prone to argue that there is no provable deterrent effect. My response is: So what? Even if there is no deterrent effect, the death penalty is still perfectly appropriate.