Since we're not looking at incidents as for the number that happen but as to the inevitability of them happening, what about the cases where a person sentenced to death is later proven to be not guilty. Once shot it is too late. Therefore the appeal process that makes the death penalty so expensive is also the insurance for society not getting innocent blood on its hands.
It may not happen often, but it does happen. At least with life in prison, a person found to be innocent can be released (though usually this will probably not make the person's life all that great- unless they write a best-selling book).