Sure, there is some overlap. But there are also certain traits that would mean instant elimination from the gene pool in the wild but don't matter much when a human takes care of the horse.

I'm sure that if you investigate feral horse populations like North American mustangs or Australian brambies, you will find out that they don't "get ill if they breathe wrong". Because all that did, died without leaving any offspring long time ago.

> But there are also certain traits that would mean instant elimination from the gene pool in the wild but don't matter much when a human takes care of the horse.

Yeah. They had that in the wild too.

> you will find out that they don't "get ill if they breathe wrong"

They very much do. If anything they're worse than domesticated horses.