The way we have been introduced to Carrot indicates that she is a secondary character. She has no unique design or original powers. The plot has never revolved around her, not even in Zou. It would have been very easy to focus Zou's flashback on Carrot, but Oda didn't do it. Even in WCI she was relegated to a secondary role. Characters like Reiju, Pudding, Bege or Katakuri were more memorable than her. She is just another ally, just like Cavendish or Barto. She lacks the depth and development needed to be a protagonist. Even Pedro was a more interesting character than her.