Mostly because the horse was a rich person's toy that most people could not afford. Horses as farm animals was only really a thing for maybe 70 years, for most the ox was much better: it ate less and was more mild mannered. The American prairie need the faster speed of the horse to make the plow needed work, otherwise they wouldn't use them. Coyboys also used the horse for roundup, both niches that started in the mid 1800s.

My grandpa remembered the horses and didn't miss them at all. They had an ugly temper and you had to feed them daily even if you didn't leave the farm. They were purely a cost sink worse than a car or tractor.