> I would be quite shocked if increasing the number of people who can go see a doctor, for free (or some incredibly reduced rate), somehow resulted in doctors working less.

Preventative care is far easier than complex "shit, you've got stage four cancer because you didn't get that lump checked out". For uninsured folks, ERs wind up functioning as primary care, which is immensely wasteful use of resources.

> If you assume medical corporations desire making more money, then they would already be looking into this step.

They are. Some hospitals hire scribes for doctors, for example.