The thing that's always glared out to me regarding sports, is that you never see them in sports that aren't divided by sex.
Equestrian sports are a good example, but if I bring that up people claim that's because trans people are more likely to earn less - the reality though is there isn't going to be much cost difference between equestrian and other sports at the top levels. Karl hester learned to ride on a fucking donkey because his parents couldn't afford any kind of actual riding lessons and in 2012 took Charlotte Dujardin to the Olympics and broke records for her gold medal performance. A lot of higher level competitors ride other people's horses and never own one.
I personally am not rich but I've spent the last twenty years around horses, I've had my own, I can handle ferral colts, at one point I was jumping decently, I've had dressage instruction from an instructor who was taught by Karl Hester aswell.
I learned to ride western which isn't common in the UK (for none horsey folk, western is how you'll see them in a cowboy film sort of thing), western is what I'm best at and it never cost me a penny to learn or get involved with. If I wanted to now I could probably earn money teaching others in fact.
Anyway, the point of this me-rail is that despite there being sports that are accessible and not separated by sex , where their trans status wouldn't get them attention, controversy, where it wouldnt matter if they were built like a brick shithouse, I've never seen a trans person involved in one. But then, it also wouldnt affirm them or enable them to access women's spaces, and they don't have an advantage over female competitors. It's easy to see where the motivation is.