Almost every county fairgrounds in Indiana or Ohio was built primarily for horse racing, with the track naturally taking up a huge amount of space. This isn’t strictly a Midwestern thing: the fairgrounds in New Orleans is similarly built around a race track. Santa Clara County’s used to have a race track too, but it was removed due to disuse as the county grew more urban. Neighboring San Mateo County turned its race track over to housing developers a few years ago.
But I fully agree that not every fairgrounds must be about horse racing. My point is that they typically serve two purposes: event rentals and gambling on the one hand, and sporting events on the other. Taking the annual county fair as an exception, the events and gambling are indoors while the sporting events are outdoors. I’m inclined to treat the fairgrounds as a “campus” for sports that contains buildings for other purposes.