I always thought this, given what i see from the records of both horses IRL, accomplishment and story.
It makes sense that Tazuna behaves like this because the IRL counterpart has a lot of health problems despite being a horse that wins everything in the short time he has. She doesn't want the other Uma's to suffer what she went through in her youth, probably.
It make sense also why Aikawa behaves like that, because the IRL counterpart just dedicates himself to being chill and enjoying his life as a rich horse in a private but boring farm owned by his owners until he adopted a random cat that one day pops out. So Aikawa is just wants to spoil the umas on her academy so they enjoy the same type of adrenaline in important races like she did in the past.
Honestly, it gives fuel to a good fic about them.
There is also a probability that the academy existed in her youth and was part of Aikawa's "family", but since she couldn't run it been "Northern Taste", an Uma, she had to hide it behind the name of her family, "Aikawa". Meanwhile, she employs her retired best friend, an uma who used to dominate all races, but retires due to an injury, Tokino Minoru, as her right hand, but has to be under a different name, "Tazuna", which means "Reins" in Japanese.
