And this indirect effect, even when the person sentenced to death is undeniably guilty:
Opportunity cost. The legal process of appeals that goes on before a convicted person is actually executed is more costly than life imprisonment. The money spent on that process is not spent on constructive public good.
I only wanted to point out the hypocrisy, but you make a good point:
I forgot:
And this indirect effect, even when the person sentenced to death is undeniably guilty: