Mildot, I think you are confusing the open/local level "all arounder" with the breed show AAs. A TRUE breed show all-around horse is definitely a hot commodity, and can cost quite a bit of money. These are the horses that go all day and stay strong. Showmanship, HUS, HSE, sometimes the hack, WP, WH, WR, Trail. Those are the main classes the AA horses go in. And to be competitive at the breed show level in those classes takes a lot of horse, a lot of time, and a lot of work. A horse that can do all of those classes and do it well is a very special horse..
Regardless of all that, those breed all rounders will be attractive only to those who show only in breed clubs.
No serious eventer, for example, is going to even consider an AQHA all-rounder for their sport. Same goes for people who are serious about jumpers, hunters, or dressage.
I don't know much about western sports, but I bet those who are serious about theirs will want a specialist too.
Point is, outside the breed community, I don't think there is much of a market for the so-called all-arounders when it comes to serious sport horses.