Asmit, you're mixing up two separate issues.
The point is, yes, there is a BYB problem with horses, just as in dogs.
Can you sometimes find gems from undistinguished lineage? Well, sure. Lendon Grey kinda made a career of that, among others.
You can also find a fabulous dog from a shelter, sometimes. One that is healthy and sound and talented at some sport, I mean.
But, that doesn't mean the breeding programs that produced those animals should ever be encouraged.
Neither should a breeding program that has lots of flash and fancy, but produces crippled cariacatures of sound, working horses.
Witness most halter programs--and esp. futurity halter, such as the AQHA program, for one example, and all that ensues from pursuit of glory in that arena.
Was never involved in the other sports, but did meet a few national level halter AQHA mares. Ones who were on actual steroids, enough to the point where they could actually no longer reproduce. The horses were almost not horses. Just like in dogs, I think there are a lot of breeds being 'overdone'.
I just have a bit "less stock" in 'well bred' hunter/jumpers anymore. Have many friends with horses worth 10-15x the value of my car, and when looking at the horse as just a horse, I really don't see it. I don't think that is 'right' at all. Especially considering the amount of wasted money they gave to some greedy breeder who is pumping out "well bred" horses left and right.
I honestly have not seen many horses competing around here that are also being bred and therefore being considered BYBs. Now as far as general purpose horses, yes definitely. There are tons of bafoons breeding horses for the sake of breeding, and they end up in the local rescue which is also ran by bafoons. (Granted bafoons that have their hearts in the right place most of the time).
I guess I just do not know of many people competing with horses of unknown pedigrees and then breeding them? I could probably find a couple, but the 7 years I competed, I maybe saw one hunter/jumper breeder that I would consider a horse BYB.
You mentioned 'greeding' in a previous post, and that was the original turn I was trying to take that post but somehow got lost in translation
I've seen many many many more large scale greeders in the hunter/jumper scene than simply just your average BYB slapping a couple horses together.
However, as someone else mentioned, there is far fewer horses out there being bred and thrown into shelters. Guess its a good thing horses only have 1 foal.
ETA None of the horses from my past have been purchased via encouraging their breeding. Most are/have been OTTB's, 'freebies', or young prospects from large breeding facilities that weren't apparently "up to par". My trainer/barn owner always said 99% of horses have no right being bred. So I guess because of her feelings, I was kept pretty secluded from the BYB horse breeding crap.