It's bizarre that these discussions seem to start from the assumption that we got here intentionally by only making good decisions.
Regulation, left unchecked, favors constant indirect damage from shortage to more visible direct harms.
This is why it takes 3000 hours of training to cut someone's hair.
The lack of doctors allows hospitals to charge more money for access to the ones they have. And right now the government foots the bill for training new doctors.
If they funded new residency slots they'd simultaneously increase their expenses, and reduce long-term revenues. Even if the resident's work is profitable by itself - in the sense of generating more in billings than the costs in salary, benefits, and teaching time - it could be bad for the hospital in a decade or two.
If the government simply ended the practice of funding residencies then hospitals and the rest of the medical establishment would be forced to come up with a new approach. Until then they're content to ride the gravy train.
But, the fact that hospitals don't fund their own seems to prove the underlying assumption - that offering a residency is a net loss to the hospital. If that weren't true, they'd fund the slots on their own.