If a horse is substandard for the use that it was bred for, a breeder might want to prevent future breeding to protect the reputation of the sire and dam of that horse.
Say you have a champion show horse. You breed him. All of his foals turn out to be show champions but one. That one is a dud. If it is going to shows and the owners are bragging that its sire is the formerly mentioned champion show horse, then other people might not want to breed to him.
You can't ride papers anyway. I wouldn't be that worried about it if it is just a horse that you want to ride and enjoy.