I loved her character and if I'm honest; I had a crush on her when I was a kid (and still do). I was sorry she left the show. I did read her book a few years ago and if I remember correctly she was devastated at being let go from Star Trek. She says and the early promo photos bear out that she was one of the intended original "big three" which of course eventually became Kirk, Spock and McCoy.
The Doctor and Yeoman characters have been a part of Star Trek since the beginning. The doctor character has always been a sounding board/adviser for the Captain, so its doubtful that the Yeoman was intended to be the third of the "big three". Probably the doctor and the yeoman were both meant to be secondary regulars, but once the show got rolling I think they realized the yeoman role was pretty limited and better served by guest stars, day players and extras. Whitney was probably in the promos because it never hurts to include a pretty girl.