Here's a better solution: let students plagiarize all they want. When they are about to get their degree, do an en masse review of all incidents of plagiarism for the student and, if it's egregious and beyond doubt, retroactively fail them for everything. The university keeps their tuition dues and the student gets what they're due.
And then the university loses all that tuition handling the lawsuits from the families of all those failed students, and due to the age of the cases/faculty leaving/etc., the case becomes hard to win for the university. Losing all around, unfortunately.
Unfortunately, you're probably right. The "shucks, if it weren't for you meddling professors I would have graduated" version is unlikely to happen in the real world.