Findeight’s examples are akin to the Brett-Ohio issue, where pedigree is unknown or turns out to be different than advertised. The issue with the hunter bred quarter horse is that pedigree IS known and IS NOT full quarter horse pedigree, but is allowed to be advertised as a full quarter horse. This would be similar to the ASB being allowed to be considered full Arabian.
The question at hand is: Why aren’t quarter horses more popular in the hunter/jumper ring?
The answer, as you, Equino noted, is that 8 out of 10 are not suitable.
Those that are suitable do not fit the quarter horse breed standard. The fact they are almost all 50% thoroughbred, helps illustrate this.
Breed standard is 14-16 hands, stocky, short cannon bone, compact. Can run the quarter mile faster than any other horse.
While the examples listed here are nice horses, they do not fit the breed standard.
This is not the opinion of a few ‘uninformed’, but the opinion of quarter horse breeders as well and is why the Foundation Quarter Horse Association was created relatively recently. The quarter horses that do well in the hunter/jumper arena are not full quarter horses. This does a disservice to the true quarter horse type - which when the registry was created, thoroughbreds were only allowed in if they fit the quarter type. Now, they do not need to fit the type. Not giving a nod to the thoroughbred influence that changes the horses type to allow it to excel in the hunter ring also does a disservice to the influence of the thoroughbred.
Some links to help illustrate:
http://www.bhfqh.com/
http://www.diamondhquarterhorses.com/American_Quarter_Horse_History.html
http://www.diamondhquarterhorses.com/