I don't understand what point you are making.
Are you claiming that one of the extremes "works"? That the "light punishment" route reduces cheating? Or maybe has no effect on cheating?
There are two extremes; I am not arguing that the one extreme (terminal punishment) reduces cheating, I am saying that the other extreme (light punishment) does not reduce cheating!
You say that stiff punishments have no effect on the cheating rate, right? Compare to what exactly? Compared to no punishments? Compared to light punishments? Compared to medium punishments? Compared to heavy but non-terminal punishments?
Now that I've reread your comment, I'm extremely skeptical that terminal punishments have no effect on the cheating rate compared to light punishments or compared to medium punishments.
It's an extraordinary claim, so I want to see this "lots of evidence"; the evidence should basically show no correlation between cheating and punishments.
I want to see that chart you base your belief on.