For the most part these "studies" that suggest a doctor shortage have been politically motivated and poorly designed. There are interest groups that want the US to increase med school and residency slots for their own benefit and there are groups that want licensing boards to concede doctors can't do it all and throw open the doors to other fields. Politically motivated "science" is the worst kind of science.
The consensus within the medical community is that there is no shortage and that the problem is one of distribution/allocation. It's a much harder problem to fix. It means you could double the output of doctors and you'd just worsen gluts in some places without fixing the problem. You really can't force people on a high powered career trajectory to go live on the farm, exchanging healthcare for fresh eggs. So all you can do is recruit people from these communities who might go back, and otherwise try to entice people to relocate to these places. As mentioned though, the money might be better spent building malls, ballparks and airports than offering them up as salaries.