Regarding the central issue, you seem content with the claim "accidents happen" when I talk about people like Henry Ford, but then you seem to think that "accidents happen" no longer applies in the criminal justice sphere. When I drive a car or walk on the street I am at risk of injury or death. When I live in a society I risk being falsely convicted and fined, or imprisoned, or in some societies, killed. It does not follow from any of this that we shouldn't have cars or criminal justice systems.
The strange modern premise is present in your thinking, but more obviously present in
@TLK Valentine's thinking. It is the premise that, "If it isn't perfect, then we should get rid of it altogether." But this is such a strange and unrealistic idea. Imperfect things can still serve good purposes. If they can't then we're doomed. We should not be asking the question, "Is it imperfect?" The question we should be asking is, "Is it too flawed to exist?" This is especially true when we are limited to secular reason.
And sure, you can just cling to the alternative of life imprisonment, but clinging to it unthinkingly, at any cost, will cause harm in the long run. And I think many cling to it unthinkingly. In any case, those who lived and live in societies that are not capable of enforcing life sentences often found that capital punishments, while imperfect, are more than justified in their existence; just as we have found that a criminal justice system, while imperfect, is more than justified in its existence.