If you consider being a Captain of a starship to be the most sensitive and hazardous of duties, it isn’t hard to imagine that women might be barred or not meet the criteria for that sort of command. I could surmise that they may have been allowed to command early on, but that the higher rate of disaster (say, loss of ships) amongst female Captains provoked the decision (controversial, to be sure, but there it is). As an example, let’s say 25 ships are sent out, 18 are commanded by men, 7 by women. Of those commanded by men, 3 meet a fatal end, but all 7 of those commanded by women are destroyed. What conclusion and decision would you make if you’re in the Admiralty ?
Of course, there’s also a contradictory version presented in the pilot episode where the female Number One was clearly “in command” during the kidnapping of Captain Pike.
Even if such an unlikely event happened (I don't believe women couldn't competently Captain a starship and I'm not even a lib, we have chicks commanding stuff nowadays, are they all failing miserably?) the PC LIB Federation would never draw that conclusion and make the decision to outright ban vaginas from the Captain's chair, even a more common sense orientated government would be unlikely to do that.
And as you say any woman who's an officer is in the chain of command and could end up in charge of the ship. It just doesn't make any sense.
Do we really want that to be canon because of one line from one silly (but enjoyable) episode? All of the things that might be wrong with this show I don't know why that would bother anyone.
There are 2 choices, take Janice Lester's statement at face value and try to make a ban on female Captains fit into the narrative (I can't make it fit for me) or do a very soft retcon chalking it up to Janice being nutso, and she WAS seriously nutso, so that's an easy choice for me.