I was traveling and encountered some Canadians. Their daughter is in med school in Canada. Costs ~$400 (Canadian) per semester. She is going to become a doctor without the massive debt most med students in the US incur. Therefore, she can have a smaller salary and still be living quite well.

But that doesn't save you any money.

Sure, you're no longer charging the med students for the cost of running a med school. But that just means that you have to ask taxpayers to cover the cost of running the med school.

The total cost to the overall system doesn't change. Whatever costs the national health insurance program would save by being able to pay doctors less for the portion of their salary that covers medical school (which is non-zero, but not especially large) just gets added back in by having to cover the cost of medical school directly.

As for medical malpractice, that's a relatively small amount of healthcare costs. It was about $55 billion (costs of both liability insurance and defensive medicine) back in 2010, or about 2% of national health care expenditures back then:

pmc.ncbi.nlm.nih.gov: National Costs Of The Medical Liability System

So maybe you can shave a percentage point of health care costs by reforming the legal system? Probably not, once you factor in everything - but whatever you can save won't be much more than a rounding error.