Nerys Myk is right. According to
Inside Star Trek, the network actually quite liked the idea of a female first officer, but they didn't like the married Roddenberry casting his mistress in the role. But Roddenberry couldn't admit that, so he claimed that he was forced to drop the character because of sexism.
After all, this was the time of
The Avengers, where Emma Peel was every bit as tough, smart, and capable an agent as John Steed. Similarly, Agent 99 on
Get Smart was the most competent character on the show. And on ST's sister show
Mission: Impossible, Cinnamon Carter's primary role may have been as a vamp and seductress, but she was also shown to be smart, courageous, resourceful, and able to hold her own in a fight.