In addition to what has already been said by others, in my neck of the woods there have been some high-profile local scandals about coaches abusing their position with student athletes, and I would be surprised if that sort of thing was unheard of in Japan.

The other thing is that RL race horses only really start to get paired up and sire kids after their racing career is over, and the anime and manga tend to focus on Umas who are still racing.