So they most likely don't mix other breeds like leghorn into their lines.
It's more about the selection process?
As I said, different hatcheries can have different policies. I can't speak for all of them any more than I can say that every cop in the world is a bad cop or every school teacher in the world is a good school teacher.
There are a lot of downsides to them mixing in a different breed, even a carefully selected breed that shares a lot of traits. A leghorn is going to be a lousy choice anyway. They are so different in size, body shape, egg shell color, ear lobe color, and such that those effects are going to be pretty obvious in the next generation and for a long time. It would be a horrible business practice. It fails the common sense test pretty dramatically.
After a certain amount of inbreeding a flock can lose fertility, production, and disease resistance. With the pen breeding method, as long as you have enough numbers this loss of genetic diversity is pretty low. You can go a long, long time before there are any effects. Many breeders handle that by using a different method, often spiral breeding. Loss of genetic diversity is a real thing but there are different ways to mitigate it. That's one reason poultry specialists study genetics, to understand how to handle those effects.
If their flock every shows signs of losing genetic diversity all they have to do is bring in birds of the same breed from a different source. That eliminates the inbreeding problems. Fertility, production , and health improves. And the general body shape, egg color, feather color, and such stay within limits. But no, they will not be show quality.
Even if you feed a hatchery bird a showbird diet, you are not likely to get one as big as a champion showbird. Hatchery chicks are not bred for that.
Folly makes a lot of good points. Even top-notch champion breeders hatch a lot of chicks that don't meet SOP standards in some way. One breeder on this forum said only 1 in 5 of her chicks meet her standards. Another one said it was only 1 in 10 for him. That's with championship breeders selecting which rooster gets to mate with which hen.