Society benefits by not having ti pay to keep convicted murderers (and rapist in some states) in prison for decades when they have no chance of every getting out.
Other prisoners benefit by having a decent chance at rehabilitation as people convicted of writing bad checks won't be housed in with serial killers and rapist.
If done correctly swift death sentences will deter others from doing similar acts.
The death penalty is more expensive than life in prison.
Bad check writers are not housed with serial killers.
The death penalty is not a deterrent.