I wouldn't say that they are the most common equid in US zoos, but they are an SSP species which means they aren't being phased out of AZA all together, but examples of zoos that had them in the past that no longer have them include San Diego Zoo, San Diego Wild Animal Park, Los Angeles Zoo, Lincoln Park Zoo, Dallas Zoo, and Philadelphia Zoo but then again for some reason I don't see those zoos getting them back anytime soon if even at all, for US zoos that currently have them, all that really comes to mind are Cleveland Zoo and The Wilds but there is probably more
As for other subspecies of Equus hemionus, the only other one that I know of in North America currently is the Kulan (Equus hemionus kulan) at Lion Country Safari along with places in the private sector
But regarding subspecies of Equus hemionus besides Onager and Kulan, Syrian wild ass (Equus hemionus hemippus), Indian wild ass (Equus hemionus khur), and Mongolian wild ass (Equus hemionus hemionus) I am not aware of any ever being imported into North America, but I can't confirm that