And the evidence to back that up is.... no female captain in Star Trek until Star Trek IV: The Voyage Home almost two decades later. If gender is not an issue, why the gender swap? If Janice is so freaking crazy, why is that made a bigger issue than simply brushing off the sexism away as nothing?
How about Number One from The Cage? Granted that she wasn't a captain in the episode, but she was Pike's first officer and the episode made it quite clear (to me, at least), that she had the trust and respect of the crew in Pike's absence and seemed to be used to being in a leadership position. Even though it was never shown, I think we can be fairly certain that she moved up to her own command at some point before WNMHGB.