I know you said object rotation isn't a proxy for mathematical ability. But I just want to add that not all intuition is geometric intuition. And not all math is even geometric.

Of course, there isn't a switch that gets flipped which suddenly makes you "good at math". But still, I think most people with an interest can study it, learn something, and make some progress. I'm happy playing a sport, but I know what separates me from an athlete and I know I won't ever be a professional athlete.