The general reason for small bores when hunting wild birds is largely out of respect for the very limited resource that these birds represent. Killing as many as possible is about the absolute least of the objectives of any wild quail hunter, with the dogs and social graces of the experience being near the top.
Commercial hunts are a lot of fun and will be the closest that most quail hunters ever get to the pageantry of a true southern wild bird hunting experience, and that is certainly fine as absent such, so many of the great aspects of quail hunting, particularly the dogs and much habitat management, would be lost.
Of course a lighter load in a 12 gauge is equivalent to a small bore, and no doubt many private landowners would understand and appreciate such a gun and load, but the commercial spots are making every effort to recreate the wild bird experience for as many hunters as their business model requires. Their hunts are not regulated under the same seasons and there are no bag limits, but the effort to provide as near of a private plantation hunting experience as possible generally includes the preference for small bore shotguns, to often include no semi-autos.