Very odd discourse here. OP, what is your point? Horses should never be bred?
I’d say that horses amongst any of the domestic animals have the most attention paid to bloodlines and genetics. Beef cattle secondary to that.
When I was in my early 20s, I met a guy. We fell in love and we got married and had a couple of kids. I certainly did not do a genetic work up of his family tree before we decided to have two children that have turned out healthy and wonderful. I myself was fortunate to have two very easy pregnancies and births. The experience of the first certainly did not preclude me from going back for another child.
Pigs, chickens, sheep, and goats? Perhaps I can become more educated, but I highly doubt there’s a stud rooster out there that people are clamoring to breed too. Animals are bred and produced for food primarily and with the case of horses, recreation and sport for the most part these days. Careful breeding for centuries had led to the likes of Secretariat, Sapphire, Totilas.
I myself kept chickens for years and every now and then a chick hen that I purchased turned into a rooster and it would breed with my broody hens and then I’d have more chickens. Neither hen nor rooster seemed overly concerned that I was forcing an unnatural pregnancy on it.