The residency slots are so limited right now because the AMA lobbied hard against expanding them in the 1990s (fearing a "glut" of doctors).

Edit: Every time this comes up I go down a rabbit hole of looking for an article from the mid-to-late 90s where a medical lobbyist spoke about how doctors would be forced to leave the profession and do "mundane" jobs like driving cabs if the residency slots weren't capped. It did not paint the lobby in a good light, and I've love to see it trotted out today. I never have been able to find the article online. If somebody with better search-engine-fu than me can find it I'd be greatful.