Health, on the whole I would agree with your recommendation that a dentist could do an extraction, but since Litvos says that the teeth are already impacted, this may require more digging to remove the teeth (sorry Litvos, don’t want to scare you).
A regular dentist, who spends most of their time with fillings and other regular dentistry activities, may not be able to deal with such a situation as well as an oral surgeon, who would have more experience dealing with these issues, as they deal with them more often in their daily work. I think in this case he could try to find out prices from different oral surgeons before emptying his wallet at the nearest one, but it does sound like something that needs to be handled in the very near future.