I live in proximity to some fairly remote ranch country and there are still a lot of pretty basic trail and using horses coming out of there. Also there are some commercial QH breeders up there who overbreed and then cull their young stock to the auctions up North. Several of my friends have gotten fairly nice QH youngsters with no papers that way.
In my general region QH are much easier to find and much cheaper than WB. Even a kind of mediocre WB carries a price premium over a TB, QH or Appendix of equal or even better quality. QH are I think the largest registry in North America.
As far as my comment on piggybacking. Quality WB breeding is driven by the European breeders that stand stallions and broodmares and are relentless about their lines over generations, and there are also big breeders doing this in North America as well. The existence of these high quality long term well thought out programs allows smaller breeders or ammies to buy sperm from excellent stallions that are the result of decades of effort, performance, evaluation, etc. It lets small breeders who aren’t in a position to run a full scale breeding operation and build a line over years and years to have access to quality sperm that they can mix and match with the mares available to them.
But if the European WB breeders hadn’t put almost 100 years into breeding modern sport horses, with rigorous selection criteria and state support and focus, those horses would not exist and none of us ammies or small scale breeders would have access to the AI sperm of such excellent horses. Because they wouldn’t exist.