> Do you have any idea what limits residency positions? They don't pay like a doctor but they do doctor like stuff. I would think that hospitals would want a lot of them. Sort of like how in science post-docs are hired everywhere because they are just the same as a research scientist, but you can pay them less.

It's the other way around. Resdiency positions are extraordinary expensive to offer - remember that this is where doctors actually receive their clinical training. Medicare funds them, because otherwise hospitals would have no incentive to offer them (they would lose money on each resident).