Can the AMA prevent hospitals from creating residencies with their own funds? I'm ignorant about this, but at first blush it seems like doctors must be a top expense and most companies enjoy employing workers with cheap wages and long hours. Hospitals should be happy to hire as many residents as possible (even if they got 60 hours from them instead of 100). What am I missing?

They can encourage their members to avoid those hospitals.

Most doctors don't work for the hospital. That's one of the many reasons behind the strong opposition to Obamacare the creation and consolidation of regional medical systems is making more doctors salaries employees and reduces their bargaining power.

My understanding is that their control to the end of limiting the number of doctors is exerted way back in the part where they have to approve new medical school seats.