Medical school and residency spots are controlled by provincial governments, and even the provincial medical associations exist at the will of provincial governments.

I don't know enough to comment. I believe groups like the CMA would have their voice heard in such conversations.

Any government that says "we recognize a sizeable portion of Canadians don't have a primary care provider (like a family doctor), that is a major healthcare problem that costs the system a great deal of money and other problems (e.g., overcrowded ERs), and we're going to start graduating more physicians this year to meet Canadians' needs" - would receive widespread approval I think, and from any party. I think physicians' lobby groups however would do/say whatever necessary to kill that.

The CMA sold their wealth management company, MD Financial Management, to Scotiabank in 2018 for 2.6 billions dollars. The CMA has been touring with the Globe and Mail over the last year to promote healthcare privatization (example).

Requiring proof of a causal relationship may be setting the bar so high that it can't be cleared.

I think there's an abundance of moderately strong evidence that the CMA has its members interests at heart, not Canadians who rely on public healthcare.

Here's the Ontario MA's statement on fixing issues in primary healthcare. They note 2 million Ontarians don't have a family doctor. Where on the list of their proposed solutions is graduating more doctors?: https://www.oma.org/advocacy/prescription-for-ontario/prescription-for-ontario-doctors-solutions-for-immediate-action