You just described 2 of the ways that the competition is being limited by law and politics: 1. Controlling the number of doctors graduating per year. 2. Making medical training very long and expensive(even when it's not needed - for example when nurses can replace doctors) so that doctors would inevitably charge higher rates in the future.

Since medicine historically was distributed and built by community doctors , the classic competition limiting strategy of using big monopolies didn't fit here.

So the medical profession uses many different strategies for limiting "distributed" competition.