Personally, I think that breeding an H/H, and possibly even an N/H, horse should not be allowed in either AQHA or APHA.
When I was sixteen I purchased my first horse (after riding them since I was 7, and leasing two of them). She was an 8 month old APHA filly that I had planned to training myself (I was in WAY over my head, but that's a different story). Now, I had been a Hunter/Jumper rider all my life, and had ridden Warmbloods and Thoroughbreds almost exclusively. I had very little knowledge of the Paint world. Being young and dumb, I purchased this filly without doing much research on her.
Fast forward three years, and I realize this isn't the horse for me. She will likely never be competitive in the H/J ring, and that's what I love to do. As a 19 year old college student, I simply cannot afford a horse that I can't enjoy. So I try to sell her.
Needless to say, there are lots of crazy people out there, and I dealt with a whole handful of them.
Finally, I found someone interested in Mia as a low level Dressage mount and possibly for driving. Her first issue was that her horse horoscope didn't match up with the ladies (What?!) But she seemed to get over that problem, and we made all arrangements for her to purchase and pick up Mia.
The day before she was set to leave, I get an e-mail about HYPP. Apparently Mia's sire had it. He must have been H/N. I had never heard of this before, but the woman flew off the handle at me. She tried accusing me of lying to her about it, of being a bad person, the list went on and on. Yes I should have done my research. Yes, this something I should have known about. But no, she did not have the right to react the way she did. A simple "I have to pass on this horse for 'x' reason" would have sufficed.
I hurriedly did my research, read as much as I could on it. I contacted her previous owners (who claimed they knew nothing about it... But I find king of hard to believe, as they are very active in the Paint horse world), as well as the studs owners. I had her tested, and she was N/N.
So, yeah. That's where my feelings about HYPP stem.
I think people who knowingly breed H/H or H/N are selfish, and there is often dishonesty involved.
A foal's status DOES matter to me, as it could effect the quality of it's life for the /rest/ of its life.
I would never buy an H/H or H/N for breeding purposes. It should be something that ends here, but people are greedy.
Granted, this all happened a few years ago. (2. Boop.) I hope things have changed for the better.
The sensitivity of the internet baffles me.