Well,there are lots of stories about why her character was cut, but the reality was problem several things, starting with money.
Yep. She had been signed to a 13-week contract, but the writers had been unable to feature her in every episode. She used to say how her two least favourite episodes were "Dagger of the Mind" (in which a meaty part for Rand had been given to Helen Noel in a rewrite) and "The Galileo Seven" (the 14th episode, in which Rand was suddenly... Yeoman Mears).
Uhura was a "day-player". Much cheaper!
Whitney had a contract to appear in 7 out of 13 episodes. She was never planned to appear in all 13.