> doctor's pay is not enough on its own to explain even a small fraction of the cost problem

Not on it's own, but doctor shortage can still contribute to medical costs.

Do doctors make more mistakes due to high patient loads?

Are preventable items missed because doctors can't spend enough time with patients?

Would people be less likely to abuse the ER and/or wait to address conditions if they could get a primary care appointment more easily?

If doctors had a little more slack in their schedules, might they innovate in other ways?

If we had more doctors, would it be harder for mega-hospital chains to gobble up the supply of doctors in your area, leaving more independent practices to innovate in other ways?