Artificially restricting? Could you elaborate? I was under the impression that the only restriction on the number of doctors is the ability for people to get through med school.

There's a fixed number of seats in medical schools and a fixed number of residency slots. When you add foreign doctors that would like to practice in the US to medical school graduates, there's less residency slots than doctors that would like to take them.

Most residencies are paid for by Medicare. Big hospital systems just can't seem to find the funds to train doctors on their own.