I think that there are so few because, as said, the good ones get put to breeding, and the mythology, in this country anyway, that a lot of less good riders have that they aren’t as good.
I think the statistics on the World Cup for show jumping is that the most likely horse to win is a Holsteiner mare. I think for show jumping and eventing there is probably less prejudice, or none.
I think some of it is the amateur attitude a lot of people seem to have that you have to have a dead calm horse, at least in dressage. These are the kind of people in the sport who never leave the ring, would never consider a gallop on the trail or jumping, or doing anything fun with the horse. A lot of the sport caters to these people, and a lot of trainers make the most money off of these people.
I prefer mares. As said, they tend to give 100% or nothing. You don’t get the super steadiness that may win at the lower levels, but you have the fire and brilliance that can do well at the upper levels. The first horse I bred was a mare and I took her to GP. She could be a pain in the ass and would just randomly explode and fling herself about, then get back to work. In her pasture she would do her daily runs and speed in circles while all the other horses stared at her. She was also jaw dropping in the ring. Chelsey (Sibley) used to ride a jaw dropping mare that was spectacular. She did NOT take her to young riders, but chose a less spectacular, but steadier gelding because Chaam would have similar episodes.
There are definitely a lot more mares now at the top of the sport in dressage, but because of the stress on dead on steady horses, I think if it makes that much difference to win at the very top, people go for the gelding. Anky rides stallions, but the geldings have done better. Ravel was apparently an easier ride after gelding. The top riders I know looking for Olympic dressage mounts tend not to go for mares, though maybe below that level of what you want to do doesn’t matter.