I have no issue with a patient requesting a physician anesthesiologist. I'm simply pointing out that there are logistical problems inherent in those requests in some practices. My guess would be that it's easier to accommodate in an an academic environment than private practice.
As far as pediatric anesthesia cases specifically - these types of cases by their very nature are "team" cases. I can do an adult anesthetic start to finish without the involvement of another person (illegal in my case, but just for argument's sake). That is not the case with a pediatric case, because someone else is going to have to do something with that patient. I can't manage their airway and start the IV by myself. Someone else will have to start the IV, or hold the mask (poor choice). In a care team environment, there will always be two anesthesia professionals involved. In many of our rapid fire ENT cases, there are two in the room the entire time, because it's virtually impossible for a single person to do everything (airway, IV, drugs, charting, etc.) during the actual case time. So even if it's a board-certified MD-provided pediatric anesthetic, somebody else will have to be involved - nurse, resident, anesthetist, another MD, whatever.