You seem to be confusing amount of money with actual control. Electrical contractors can charge any price they want (subject to customer demand). Hospitals, especially teaching hospitals, have no such freedom. Medicare reimbursement rates are fixed by government fiat. This is not a free market.

Residencies are already chopped up into tiers. Those with more experience have more clinical and administrative autonomy. But for the most part, Medicare doesn't allow hospitals to directly bill for work done by residents. With a few limited exceptions, all of their work has to be supervised and signed off by a qualified attending physician. This training and supervision is extremely expensive.

Any major reforms will have to come at the federal government policy level. This is not a problem that medical schools and teaching hospitals can solve by themselves.