It is not just that race horses and a lot of other 'working horses' are all business and are not pets. It often does not help the buyers and their trainers to interact with these horse a lot before they change hands.
When I trained and fitted race yearlings, I was very strict about good manners and good ground schooling. Unlike a lot of other breeders and fitters, I trained them all to tie, to stand good for trimming, clipping, bathing and grooming. They all stood still when told to, led anywhere, backed up or mover over when asked, but that was where their training ended unless we were hired to start them under saddle later. They all led quietly in a halter with and without a chain over their nose and they all were trained to lead in a Chifney bit. They had to handle well for their next handler.
I had to present some of them at the sales and others were picked up by the owner or a Van and shipped to the sales. They were always led through the ring by a total stranger wearing a white coat. Others were fitted and sold 'private treaty' to people came to the farm to look at them. We were always complemented on how they looked and how they were handled. The idea is to please the person writing the checks.
My help could go in and get any of them and turn them out for exercise, get them in and groom them or bathe them, brush out their manes and tails, and in general, handle them like any show horse.
I did not let them do a lot of petting and they were absolutely not to give treats or hand feed any of them. They were strictly to be treated in a kind but business-like way. No one was allowed to pet or feed horses that stuck their heads out over the stall doors. I had a sing in the barn the read: "Please to not pet the horses"
When someone buys a long yearling at the summer or fall sales, their trainer is the one they want to do any training other than what I listed above. They don't want to buy 'pets' and horses that have been 'over-handled'.
I know many trainers that say they would rather get in a horse that was not even halter-broke or was half-wild than one that is spoiled or a pet.