Russia hasn't been communist in that sense for decades. There are plenty of professions there that have become exceedingly wealthy in that time, but doctors have not. So to make your case, you'd need to demonstrate 1) that specific ongoing regulatory burdens in Russia have served to suppress physician pay, and 2) that the persistence of those particular burdens in Russia's era of deregulation is not linked to gender bias.
Your "seems pretty obvious to me" is <em>only</em> valid if you assume a priori that there are no distortions to the pure, free market outcome due to irrationality on the part of market participants. Systematic gender bias would be a clear example of irrationality (which I assume you'd agree with even if you didn't believe it were actually at work here). You may not mean it this way, but your phrasing sounds to me like you're assuming your conclusion.
Russia hasn't been communist for a while but almost all the doctors are still state employees. As for distortions, can you think of any other cases where the distortion is massive and the situation doesn't involve government subsidies?
Regardless, I'm not going to go digging around for evidence. My point is that the post above and the linked article did not even address the socialism aspect, which is a huge warning flag.
Your "seems pretty obvious to me" is <em>only</em> valid if you assume a priori that there are no distortions to the pure, free market outcome due to irrationality on the part of market participants. Systematic gender bias would be a clear example of irrationality (which I assume you'd agree with even if you didn't believe it were actually at work here). You may not mean it this way, but your phrasing sounds to me like you're assuming your conclusion.