"Mercy to the guilty is cruelty to the innocent."
Besides, a bullet is cheap.
As we say here, "The recidivism of those that get the death penalty is exactly 0%."
The death sentence is ugly, revolting and regretful. But in any society, there are alphas that are wired to prey on their fellow man, and they must be culled. It isn't pretty, but the world is an imperfect place.