Frumnotyeshivish, I don’t know if it’s really the case that doctors have difficulty finding jobs in the places they want to live. Even if you get a scholarship that makes you move to an area with a doctor shortage, this shouldn’t be a problem, because although rural areas usually have a shortage, so do most inner cities. The vast majority of inner city areas are within commuting distance of a frum community.
My main concern would be hours and work/life balance, since the hours are often unreasonable. But that totally depends; there are some doctors who work for HMOs or have their own practice and work a 40-hour week. Such reasonable hours just seem much more common for non-physician medical professionals.