The only other ship on active duty we see in TWOK has a .... wait for it .... heavily male-dominated bridge crew. If anything, Saavik seems unusually precocious, to the point of directly challenging an Admiral during active duty. Saavik wasn't depicted as normal at all, especially relative to the other cadets.
We're free to imagine anything we like, but what we'd actually been shown to that point didn't "heavily imply" what you're saying.
You remember The Making of Star Trek by Whitfield and Roddenberry? Only one-third of the Enterprise crew was said to be female (page 205). That's nothing you'd say about a top-of-the-line ship of an organization in which sexual discrimination didn't occur.
Before you can say, "But that's not canon," the crew being one-third female was straight out of the Writers Guide. Sure, that's not canon either, but it's proof that sexual discrimination was something that Roddenberry conceived as being integral to the premise. Roddenberry even got story credit for "Turnabout Intruder."
It was nice to finally see Star Trek's first female starship captain, in TVH.