Can't find a mare ready to arouse the stallion in time. Motility is a major factor. The ranch is too far from the vet. Too many variables increase the room for error. Time and delivery are too critical.
Complex routine is too much of a problem for the trainer-breeder.
AI has reliability problems beyond the control of the smaller operation. Too much legal and insurance hassle. Teasing is the most important and time consuming part of the breeding process. Inside breeding is preferred if hand breeding is necessary, but many people don't have the facilities. Opinions on hobbles are pretty evenly split.