Which is too bad because there are many mares that are bred that shouldn’t be.
Spaying a mare however, is obviously a more complicated invasive procedure, not really comparable to gelding.
If you look at gelding from a breeder’s perspective it is a form of culling their stock and preserving the quality of their bloodlines.
As @luvmyhackney mentioned, there are several European countries (and I think some Middle Eastern ones as well) that don’t geld as a rule, but they don’t breed the stallions that aren’t worthy of passing along their genes. They know how to train and handle stallions, a skill set that is disappearing in the U.S. and now seems to be limited to racing barns, breeding farms and high level competition barns.
Racehorse breeders don’t geld their well bred colts early as a rule, for several reasons, possible breeding in the future being one of them.
If you were handling a stallion and it jumped on top of you to get to a mare, you were not handling it properly. Stallions need to be well trained and their handlers need to see that sort of thing coming (don’t walk between a breeding stallion and a mare and, keep their attention on you ) to prevent it from happening. Handling stallions is definitely a skill, but it can be taught to people who have a lot of “feel” for horses.