The presumption is that under a "free market" the demand would drive more production - more doctors. But that the rules of the current system artificially restrict the supply of doctors. Some of that we want - credentials clearly serve a purpose - yet are the rules more restrictive than they should be? Should there be more residencies? Should we have more "lower-level" providers like nurse-practitioners, PAs or pharmacists that can prescribe? There is limited ability for the market to innovate in such a regulated environment.
Since people refuse to see regulatory capture as an unavoidable feature of capitalism.
Because it's factually not. At least, unless you define "capitalism" in a specific twisted way that includes "regulatory capture". Which I suppose a lot of socialists do...
The Soviet Union had wages to, and far worse problems with shortages then capitalistic countries have ever had.
Yes, but not in general shortages of doctors. It's a totally different problem, so this isn't really a helpful way to look at it. After all, if there's a shortage of cabbages, it doesn't mean the remaining cabbages benefit and can lobby to keep it that way!
Cabbage farmers can, though.
Yes, but when that sort of thing happens in commodities it's an illegal cartel, whereas when it happens with jobs it's responsible self-regulation by a professional association.