This woman commanded not only a starship, but a whole squadron..
But not a squadron of Starfleet starships. And she not Human. As you noted, we never saw a human woman in command of a starship, it's possible that females of other species with memberships in the Federation did have their females in command of ships.
If I'm remembering correctly, the portion of The Cage footage which shows Number One being left in command is encorporated into The Menagerie - thus including it in TOS.
A parallel might be this as far as Number One being in a position where circumstances might place her in command of the ship.
Historically, American military policy was that women not be placed in combat assignments, however in their support roles women would occasionally find themselves in combat. They would travel into the wrong area, or events would overtake them. They would be removed from the combat situation as soon as possible, they would not be simply allowed to stay in combat.
As second in command Number One could find herself in command if something happen to Pike, but would she be allowed by Starfleet Command to retain that command? Or would a new commanding officer (male) have been assigned to the ship as soon as possible?