I do think women holding thd rank of first officer but being barred from being a starship captain makes as much sense as barring them at all.
I don't think the two make equal sense at all. If women are barred completely from being commanding officer, it would only make sense if they were also excluded from the chain of command completely. It would only make sense if a male officer had succeeded to command in Pike's absence. Why would a woman be eligible to take command sometimes, but not at other times? It's not credible.
Placing women in the chain of command implies just that: They are in line to take command, period. Just like in the real world, when the US Navy allowed women to become line officers in the late '70s, it became inevitable that eventually a woman would take command of a US warship.
As to whether a first officer succeeding to command counts as being "the captain," "The Tholian Web" strongly implies that it does. Kirk tells Bones, in his recorded message, to remember that Spock "is the captain," and Scott and McCoy both call Spock "captain."
The rank of Captain has a much higher status than First Officer. It was never claimed that women could not hold high ranks but did they have what it takes to be that special unique thing - a Starship Captain?
The rank of captain and the position of captain are different. We have been discussing the position. It was shown that a Starfleet officer can go beyond the rank of captain without having commanded a starship ("The Deadly Years") so the rank is not really pertinent to this issue.
It seems pretty clear to me that "Turnabout" and "The Cage/Menagerie" contradict each other. I can also see all kinds of benefits in supporting the "Cage" interpretation and little for "Turnabout." Unless you're wedded to the idea of gender inequality in the TOS Starfleet, I'd say discard what "Turnabout" says on the subject and don't give it a second thought.