As someone who owns a registered half-Arabian, I take this kind of offensively. National Show horses (Saddlerbreds x Arabians) are a HUGE breed in the half-Arabian community. Morabs (Morgan x Arabians) make amazing mounts in the show ring. Quarabs (Quarter Horses x Arabians) make super awesome gaming or ranch type horses. Registered, quality bred half-Arabians are worth their weight in gold. The Arabian Horse Association is among the most reputable registries out there.
I own a non-traditional half-Arabian being a Rocky Mountain Horse x Arabian. Kick-butt in the show ring, an all-terrain monster on the trails, endless heart in whatever I ask of him... People who own or breed quality half-Arabians know the value in these horses.
If my rescue Morgan mare turns out not to be registered with the Morgan Horse Association after DNA testing, I will likely choose to breed her to an Arabian stud someday.
Toofine - 1998 Half Arabian
Minnie - 2013 Morgan