I know you've chosen this because you think it's a reductio ad absurdum counterxample, but really, if the market is desperately short of brain surgeons, you might think it would create more, cheaper places at medical schools.
Medicine is a uniquely restrictive market, hemmed in by legal protections and a labor guild system, but some version of this dynamic is operating in many sectors of the American economy: Companies refuse to pay for training, then whine that they can't find suitable candidates.