The other thing I do is I don't make exams so weighty. If you ace the exam but you don't do well on the assignments, you're not getting an A in the course. So the hypothetical wealthy cheater will have to keep their body double on retainer for the semester.
But I will say that the students who earn an "A" are ones I interact with fairly regularly. "A" students typically come to class, ask questions, engage with the assignments, start their assignments early, etc. And before anyone accuses me of playing favorites, I don't do any grading, and grading is anonymized. But I can easily predict the "A" students just by their work ethic. The idea of the brilliant student who doesn't come to class and effortlessly breezes through the exam is as far as I can tell after teaching thousands of students a myth. At least at my university. Maybe all of those kids go to MIT.
The distribution is one thing, but grade correlation with other statistics might be more revealing. In particular, how do you know that wealthier students aren't hiring people to take the exam for them?