Their are plenty of HORSES that are 14.2 and under. That does not make them ponies. My 14 hand arabians are not ponies they are horses. A welsh cobb or connemara pony that is over 14.2 do not become a horse. Using height to designate a pony is archaic and false.
I have seen a couple of 13.2 or 13.3 hand QHs that are registered with the AQHA. Shalom
However - in relation to this specific discussion - for a non-registered horse of stock-horse type look - anything 14.2 hands and under is most likely going to be considered a quarter pony rather than a quarter horse.
Even those breeds that are almost always considered horses no matter what the height will still typically be shown as ponies due to height requirements in the shows.
Determining what is a pony by height is far from archaic and is an active working and quite modern definition of what a pony is. The physical characteristics of a horse vs. pony (chest depth to height ratio, back length, neck length ratios, etc), metabolism, temperment, etc are not modern concepts by any means and have been around for many years. However, classification by height makes distinction for shows, etc simple and easy and a modern convenience.