> If Universities made examples out of students who were 100% confirmed cheating beyond reasonable doubt, the amount of cheating would decline significantly.
I don't think that actually follows. As I understand it, many universities and zero tolerance plagiarism and cheating policies. The problem is, when you have no middle ground and your policy is extreme, you leave yourself very few options in the cases where you don't want to or can't easily expel the student. If your policy is expulsion for cheating, then not doing so and providing a lesser punishment is seen as favoritism if the student has resources, or is used as ammunition for their own case by students with resources if offered to a deserving student otherwise.
I think the actual solution is well defined, less flexible, but not overly harsh punishments. Any student caught cheating or plagiarizing is not expelled, but immediately either fails the class or drops two letter grades (and a second time in the same class would be failing the class no matter what if the more lenient option was chosen initially).
With extreme consequences teachers are going to be hesitant to report small and borderline cases, because the consequences are so large. Make the consequences manageable for the single occurrences but problematic if they keep happening, and you'll correctly catch those serial cheaters and those occasional ones that are better off just taking the hit (and maybe dropping and retrying the class) instead of letting them slide because the punishment is disproportionate to the crime.
Think of it this way, if the crime for stealing a candy bar was life in prison, would you call attention to the person next to you that you just saw steal a candy bar? Does the store attendant actually call the police, or just take the candy bar back and tell the person to leave? What if the person is rich, and it actually causes you problems to turn them in, because it's worth it to them to make sure they don't suffer that major negative consequence be exerting their influence? If the punishment is seen as disproportionate to the crime, people will make their own decisions to avoid what they see as a problem with the system, and it also means that people with resources are more likely to exert those resources to avoid those problems, to the detriment of those around them (and they'll mostly get away with it, because who wants to die on the hill of making sure someone is punished for something so inconsequential?).