This is one of those instances where, just because we didn't see it on screen doesn't mean that it isn't so. Barring the eccentricities and remarks of a few characters, women by the 23rd century were doing exactly the same things men were (maybe even a little more as, other than one instance in the 22nd century, human men still weren't getting pregnant).
Starfleet of the time had dozens of stations and hundreds of ships and we only got to see the CO's of just a handful. There may not have been any prominent women Captain's of a Constitution-Class but that would be by chance rather than design.
In my mind at least, Number One was promoted to Captain after serving Pike for two tours, but instead of being given the Enterprise
, she was instead offered a much larger deep-range explorer (based on the designs for upgraded Enterprise
"Planet of the Titans") which would see her go further out into uncharted space than any other starship Captain. So whilst Kirk is fighting Klingons and teaching alien women to love, she is seeing things no other Starfleeter has, establishing peaceful relations with new and unusual species, and keeping the Federation safe from threats it could never have imagined. But as I said, that's just how I envision things.