One big problem with that logic is that it ignores the fact that the incentive not to go prying into a potential miscarriage of justice after an execution has o

One big problem with that logic is that it ignores the fact that the incentive not to go prying into a potential miscarriage of justice after an execution has occurred is much much higher than after a prison sentence (even life without parole) has been passed. That in turn is a problem because an innocent person convicted almost always also means a guilty person left free to reoffend.