I have noticed some talk of wanting American breeds to become similar to European Warmbloods and the way they are inspected before allowed to breed or at least allowed in the registery.
Warmblood breeds were created in the 17th century to created cavarly mounts for the various countries cavarly forces. The usual method had the king owning the stallions and either private farmers owning the mare or state stud farm. They crossed was usually a Andalusian or similar stallion bred to local mares, to create the first generation of the warmbloods. The inspection come from this state purchasing the foals (usually colts) for the cavarly service.
Quarter Horses were breed to create a better ranch horse than the mustangs that most ranches were using. Yes some ranches had well bred horses too and then crossed the on local mares. Steeldust comes to mind as one of these horse.Then with the government's remount program of the early 1900's, TB stallions were now available to create more suitable mounts for the US cavalry. Any way they was crossed to create the fountation style QH, not all had TB bloodlines in them.
These two breeds or types were created for different reasons and by very diferent cultures