For a lot of zoos it come down to space. They want to manage the animals they have and not create more unintentionally. Some of the endangered species in America have to have a certain amount of genetic diversity to maintain the population. Lets say you have two giraffes that are brother and sister. You don't want them to breed but in the future another zoo might have a giraffe they could breed to them (you would exchange giraffes). You can't afford a separate exhibit and the giraffes enjoy a social situation. So birth control for them and it solves a host of other issues. As far as castration, if you castrate a male lion he looses his mane so not many people want to see that.
At your mares age, I would look into why she is having issues. Is there a hormonal imbalance or something with the structure of the ovary that is causing the issue. I think breeding her is a bad idea. You are bringing another horse into an over populated location, your mare may not be worth breeding in the first place and its a gamble, she might produce a foal with the same issues she has and it might not change the mares situation long term.