Alternate alternate explanation: wealthier students also stopped cheating, but corruption became even more rampant in the grading stage. A lot of papers were "marked" so that they could be recognized by the graders and given a more favorable grading.

I know people which were a constant 5 at math through high school but which got 9.85 in the exam (1-10 grades at the time).

Teachers preferred corruption to happen in the exam room, since it was the students cheating, than in the grading stage where they were liable.