Here’s the dilemma. Think about human families. In most modern developed urban countries there is no linebreeding, let alone inbreeding. People marry into completely separate families, in some cases into completely different cultural or racial groups. And the children are very diverse physically. One child looks like mom, one child looks like dad, one child looks like a paternal aunt or maternal uncle or a grandparent. Talents and height and athletic ability are very different. Even when both parents are from the same general cultural group. And children can pop up music or artistic talent the parents never had.
This is wonderful and charming in human families. For an animal breeding program it would be a disaster. Breed a Percheron to a TB and you can get anything from a recognizable draft horse with feathers to a heavy hunter to something that looks like a Lusitano standing still at least 
to some surprisingly fine boned smaller kids jumpers. We have a local eventing/ lesson operation that was doing this and I have seen a lot of this cross, likely from the same stallion. Some were clearly not what you really want in an eventer.
That’s the extreme (horse equivalent of the leggy model marrying a big handsome football player where they hope the girls take after mom and the boys take after dad, which is not at all guaranteed).
But performance animals need to be more predictable in outcome. Dogs of any given breed are almost identical (unless its your beloved dog) as are Freisian horses (small genetic pool). But then so are most wild animals, even when they come from different regions, so only thinking about domestic animals. Which were bred long ago to have a huge range of diversity, and that diversity captured by inbreeding or linebreeding. If that hadn’t happened we’d all be riding Prezwolskis horses or tarpans or zebras.
So the specialized domestic animal is already linebred over centuries to lock in desired traits. Along with that comes some congenital risk as well as benefits. But breeders of both dogs and horses have ignored these to some extent, especially when the issues pop up in middle age. Lordosis in Saddlebreds. HYPP in QH. PSSM. Poor feet in TB. And the wierd things now becoming evident in WB like DSLD and shivers and string halt.
It’s true that we don’t have genetic tests or even in some cases real diagnostic tests. But they are something you might observe if you kept your own horses, and didn’t send AI semen over the world and have no idea where the babies went. Also the more a stud breeds, the higher chance somethung gets passed on.
And also some of these issues exist in multiple horse families even multiple breeds. We know where HYPP started and how to test. But PSSM has always existed as Monday Morning Sickness in the old vet books and is now known to exist in a number of distinct breeds so you could get it in a crossbreed.
I do think genetic disease is a thing breeders should be taking seriously and testing for. But when the disease is a by product of breeding for other exaggerated traits, it’s going to be a conflict of interest.
