You could be right -- there are a lot of episodes of Trek that are "why a X can't be a starship captain".
On the other hand, one thing I am finding with SF in Trek's time is that lots of people do conceive women in expanded, 21st Century (and beyond) type roles. Many SF writers don't and keep writing reactionary stuff (*cough* Silverberg) but others have woman minority starship captains (*cough* Delany).
I have always felt "Turnabout" was supposed to be about "why a woman can't be a starship captain" but that message was undercut by 1) a messy script with other factors (Janice was crazy as a loon), and 2) the actors in the show didn't really seem to be on board with that message--they undersold their key lines on that regard. I will note that the Romulans had a female Commodore equivalent several episodes before, not to mention T'Pau (though women statesmen were period to the time -- viz. Gandhi and Margaret Chase Smith).
So it's like a dog whistle. Either interpretation is possible. Certainly, the folks of The Spaceflight Chronology (1980) heard the dog whistle took it as gospel. When I get to the 70s, I'll see what fanfic has to say about it.