The purpose for the death penalty is retribution. An eye for an eye.
Incarceration for life is to keep the felon from harming society.
There is always a chance that the murderer within the confines of
prison will be able to use his life for something constructive.

There is an idea in psychology that the death penalty may offer
a better reward for a killer who often is suicidal anyway. Life imprisonment forces the killer to face the problem and not avoid it
by dying. Recidivism has no meaning if the death penalty becomes a solution rather than a transforming experience for the killer.

Frank