Some of this is an internal accounting problem. The net income (or loss) from operating a residency program depends on how you allocate associated revenues and fixed costs to it. But empirically the fact that teaching hospitals aren't all rushing to expand their residency programs indicates that they probably aren't profitable.

The value of residents varies a lot by experience and specialty. Like a 1st-year neurosurgery resident might be worse than useless and a huge burden to everyone around them. Whereas a 3rd-year family medicine resident can do a lot with minimal supervision.