> Strip congress and the medical board of their ability to control the number of residency spots and you will see the free market correct itself.

This is nonsensical. Residency spots are not controlled by the government. Government funding for residency spots is controlled by Congress, because Congress is responsible for all government spending.

The only way to have Congress less involved in residency spots would be to eliminate all government funding for residency programs, but that would have the opposite effect of what you likely want, because residency programs by and large lose money (that's why Congress provides the subsidy in the first place).