That's only true because the anti-death penalty activists do everything they can to keep murderers alive as long as possible. Even when there is no doubt of the killers guilt they will stretch it out as long as possible just so they can say "It is cheaper to put them away on a life sentence without parole than having the death penalty."
The activists don't determine the legal course of an individual. The system is designed that way so that any and all possibility of doubt towards the person is eliminated. Documentation already shows that despite our best efforts, we still have executed people that considerable doubt towards their guilt has been shown. We do that because it is a major game changer. A state that executes an individual regardless of guilt or innocence changes from a state that executes its citizenry to a state that murders its citizenry. Say what you will but the legal channels are going to stay in place and it is not the activists that have made it that way...it's the parameters of our democratic legal system.