That isn't true. Just off the top of my head, Qh's and Arabians don't allow breeding to other breeds. Well, arabians do, but they are registered as such (halfbreds) and don't get all the benefits of the registry the purebreds do. And, you don't think the gene pool is shrinking already with these shuttle stallions and others breeding to 200 mares a year? AI isn't going to change those numbers.
Uhmmm...QHs do allow breeding to TBs...and appendix registry which can be upgraded to full registry under a very clear set rules.
Per AQHA:
A horse registered with AQHA which is the result of breeding a Thoroughbred and an American Quarter Horse that has a permanent number, or a combination of an Appendix numbered American Quarter Horse and an American Quarter Horse with a permanent number. Appendix horses are distinguished by an "X" in front of their registration number and their certificates are gold.
There are three different mixes of horses that are eligible to be registered in AQHA's registry:
Registered Appendix (X) + Registered American Quarter Horse (QH) = Registered Appendix foal(X)
Registered American Quarter Horse (QH) + Registered American Quarter Horse (QH) = Registered American Quarter Horse foal (QH)
Recognized Thoroughbred (TB) + Registered American Quarter Horse (QH) = Registered Appendix foal (X)
Also, per AQHA for Appendix getting full Numbered registry:
203. TO OBTAIN A NUMBERED CERTIFICATE.
Except as otherwise limited on proper compliance with the rules and
regulations of AQHA, a stallion, mare, gelding, spayed mare or nonbreeding
mare may be registered in the Numbered section of the
Stud Book which:
((b) Previously has been listed in the new appendix, and (1) has
qualified for Register of Merit in AQHA-approved performance
events not restricted in any way (youth and/or amateur Register of
Merit do not qualify a horse for advancement), and (2) for which
AQHA has been provided a signed statement from a licensed veterinarian
in which it is certified that the horse does not have a parrot
mouth (see rule 205) and that if it is a stallion, it is not cryptorchid
(see rule 205).
(c) When a stallion or mare previously listed in the New
Appendix attains a registration number, any offspring listed in the
New Appendix shall on that date become eligible for advancement
to the numbered registry. Advancement of such offspring to the
numbered registry shall be on request from the record owner and
accompanied by the appendix certificate and payment of the
advancement fee, or
(d) Previously has been listed in the Old Appendix and which
(1) has had both parents acquire an AQHA number, unless this horse
already has been rejected on conformation inspection; or (2) has
qualified for one of the Registers of Merit; or (3) has passed conformation
inspection. Such horse then will receive a registration number.