"The AAP concludes that there is currently a shortage of pediatric medical subspecialists in many fields, as well as a shortage of pediatric surgical specialists. In addition, the AAP believes that the current supply of primary care pediatricians is inadequate to meet the needs of children living in rural and other underserved areas. In the future, more primary care pediatricians will be needed to care for the increasing number of children who have significant chronic health problems and who will require more medical and surgical care from pediatric physicians throughout their childhood. In addition, there will be an increased demand for general pediatricians because of the decrease in the number of family physicians providing care for children and the limited number of nonphysician clinicians interested in pediatric careers."
As with every career, there is an excess in highly desirable places and a shortage in non-desirable ones. Overall, I am aware of little evidence that there is a major "squeeze" in pediatrics, especially, as the AAP points out, in specialty care.
In many places family practice docs serve as substitutes for general pediatricians. As the population gets older, family practice docs will be less able to see kids as old people demand their attention.(The updated workforce piece alludes to this in a rather vague way.)
In this context (and no offense intended to FPs) economists would refer to family practice docs as "substitute goods". When substitute goods become relatively scarce, the commodity consumers really want (i.e. pediatricians) becomes higher priced.