Re: "Maybe import more doctors..."
the American Medical Association acting as a cartel to limit the number of medical schools and medical school slots in the US. Perhaps if that eased up, one could find more US-born doctors willing to practice outside the big cities.
That's not the problem. Big cities support specialists who earn more. Small towns need general practitioners aka Family doctors who don't make nearly as much, especially if they have to maintain a private office.
For US medical trainees, the obvious lure is as a specialist in a city. They then have an income sufficient to pay back their education loans, whereas foreign generalists quite likely don't come with the same debt burden, so are willing to work for less.