I think incarceration and loss of freedom/rights is supposed to be the deterrent, capital punishment is supposed to make sure the person/thing who committed heinous crimes will never have a chance to do it again or be free.
Incarceration doesn't work for all, either. In Milwaukee, murders have been committed three hours after a convicted murdered was released early from prison- someone dropped the ball when they evaluated that turd. MKE just had a murder outside of a bar, where the guy got into an altercation with someone and was shot. Once he was on the ground, he was shot two or three more times. He was a known criminal (possibly a murderer)- still looking for the link.
I would never want to see innocent people put to death and that's why any capital trial needs to be inspected and combed through, to make sure no mistakes or intentional bias exists. but, what should be done with someone who kills many, or is directly responsible for many murders?
If there's no place for capital punishment in a modern advanced society, why should murder and other terrible crimes have a place? While data shows that most violent crimes had been declining until last year, they still happen very frequently, without any sense of guilt on the part of the ones who commit them.