Lots of general dentists refer these extractions because they can't physically do them in a way that is safe for the patient. (It is an open question whether state board exams should exclude such practitioners from the profession entirely.) Introducing general anesthesia to the situation makes the procedure more, not less, dangerous. Especially in larger cities, there would be numerous dentists capable of safely performing an impacted third molar extraction under general anesthesia. Such dentists will charge for their expertise. Poor and rural patients will get local anesthesia.