Obviously, when they produced "The Cage" and gave that line to Captain Pike, they were writing to an audience in 1964, when women in the military were "only" nurses, and not front-line officers. They were obviously self-conscious of the implications of that line, based on Pike's immediate interaction with Number One in that moment. Not to mention the fact that the rest of the run of TOS had women on the bridge all over the place (not just Uhura, but many other examples.) And in post-TOS prequel series like Enterprise and Discovery, there were women on bridges all over the place. Of course, nobody in 1964 had any idea that particular episode would still be culturally significant in 2020.
Frankly I can't see Bruce Greenwood or Anson Mount (or any modern Trek writer) interpreting the Pike character anywhere close to the face-value of that particular line. So I'm wondering, how do other people interpret that particular line in that particular episode? Especially in the context of what Star Trek has become in the 56 years since "The Cage", as opposed to how it was intended for its primary audience of television executives in 1964?
I think it's pretty clear from context that in the world of "The Cage" (and remember, a lot the background worldbuilding we think of for
Star Trek had not been decided upon yet; the USS
Enterprise is a United Earth ship, Spock clearly has and expresses emotions, there's something called the "time barrier" that's been broken since the
Columbia crashed, they never established what century it took place in, etc.), women had only recently become commissioned officers of the space service (remember, they didn't decide to start calling it Starfleet until about a third of the way through TOS Season One) and Pike was not yet accustomed to their presence.
This was Gene Roddenberry simultaneously being more progressive than others of his era (women weren't allowed on U.S. Navy ships until the 1970s) yet still being pretty misogynistic (the idea that hundreds of years would pass before women would be allowed to serve in the space service is sexist on its face given the context of the second-wave feminist movement going on during the production of the pilot, and given that
Valentina Tereshkova had already become the first woman in space the previous year).
In a lot of ways, that line is like the miniskirt/skort uniforms the women wore. In the moment, in the '60s, miniskirts were empowering and gave women a sense of control over their lives and how they were perceived. By the time of the late '70s, there was a groundswell of contempt for the idea that showing that much skin could make women be seen as more powerful and in control than a more covered up look. There is no consideration for the miniskirt replacing the long pleated skirts of Donna Reed or Princess's poodle skirts and their perceived limitations, just the idea that an exposed woman is an exploited one.
Pike was meant to be saying that women could be officers, he's just not used to the idea. Our later out of context interpretation can no longer recognize that concept.
See, the problem is that you're overlooking the difference between
intent and
impact. Miniskirts may have originally been
intended as an act of emancipation, but when it's done in the context of a bunch of white guys making the women they hire show off their legs because they can't imagine a future where women wouldn't agree to be living ornaments for men, well, that's a sexist impact no matter what the intent of the miniskirts in real life were.
And as I just outlined above, something can be more progressive than is common relative to its own era, and yet still be objectively sexist/racist/what-have-you. Here's a good example: Abraham Lincoln was more progressive relative to most white Southerners since he wanted black people freed from slavery, but he was still objectively a white supremacist who didn't want black people to have the right to vote, the right to serve on juries, or political equality, and who wanted black people to leave the U.S. after Emancipation. It is right to remember how much better he was than most of his contemporaries, but it's also important to remember that he was still objectively a white supremacist, and to remember that others of his contemporaries (such as Representative Thaddeus Stevens) were far more progressive and anti-racist than Lincoln.
The Menagerie is "more" canon than
The Cage since
the Cage's ending was changed, but everything else occurred the same except some "non-relevant" scenes/lines were "not shown" in the
Menagerie's telecast. YMMV

.
Thinking about the star system names...what would Federation Cartography call star systems that they find inhabited by another people?
I mean, obviously sometimes Federation Standard uses characters from Earth languages in place of the native names of a given planet or species: I find it hard to believe that Vulcan, Romulus, Remus, Orion, Kronos, Betazed, Borg, Bynar, Grazer, Delta, Kelpian, etc., are the native names of these places and peoples, and that they all just
happen to be identical to or sound very similar to English names for Greek mythology, letters of the alphabet, terms like "cyborg" or names for Earth animals.
Would they adopt a name change from the old Earth naming system to rename stars with the name given by the inhabitants? I think they would, so for example, if we find Vega inhabited by the "My Place" people and they call their star "My Place", then the Federation would call that star "My Place".
I would hope that standard practice would be to adopt the native name rather than to impose a foreign name onto them. Though presumably they wouldn't start calling it
My Place, but would instead start calling it
[Alien Term That Translates As "My Place"].