This is not a problem with humans ability to determine probability.
This is a known issue with probability-based decisions. I known I've seen a couple studies on the topic, I just can't find a cite right now.
But that's an interesting point on people not turning in other people when the punishment is too steep. Advances in detecting cheating, and more resources spent on detecting it, may make that issue insignificant compared to the chance of getting caught by the proctor. It's an interesting thought.
Your points are lacking. Why not make cheating impractical? It's pretty easy. It also has the advantage of making tests more comprehensive. Granted, you might have less of them because they wouldn't be as easy to score.
I don't think it's as easy as you say. Otherwise, it would be done more often. It's expensive to write, administer, and grade more comprehensive exams. Given that most college classes only have 2 or 3 exams, would you really reduce the number of exams? And if fewer people are cheating, because it is impractical, then the benefit of cheating successfully increases.