It's fascinating...Carrot is the only candidate I can think of where people need to make up ridiculous headcanon in order to explain away how her joining the crew wouldn't be a natural consequence of events.
Momonosuke - As a defenceless 8 year old who is supposed to be the shogun of Wano, will abandon his country after having finally reclaimed it, in order to pursue a life of piracy in the New World with the straw hats
Kin emon - The main retainer for lord Momonosuke, having finally reclaimed his country, having witnessed firsthand the dangers of abandonment of a country, will himself abandon Wano and his vulnerable child lord in order to pursue a life of piracy with the straw hats
Otama - A defenceless 8 year old girl will be accepted by Luffy into his crew and will be well prepared to fight a Blackbeard Pirate in the near future
Komurasaki - A defenceless princess of Wano, having finally come out of hiding, reclaimed her country and reunited with her brother and retainers after 20 years will join a pirate crew!!!
Carrot - An incredibly adventure hungry battle natural that has journeyed and bonded with the straw hats to the point she is considered like family, has previously cast aside her priorities for adventure, had a "taste" of what the real world and adventure are like, had a mentor that died telling her of the importance of the straw hats, is familiar with the ship and has unofficially adopted a position onboard is just going to return to her elephant back and live as a regular mink.
![Suresure :suresure: :suresure:](https://worstgen.alwaysdata.net/images/smilies/symbols/TS96mXm.png)
Carrot's the only candidate people make up wacky ideas such as hunting down ponegliffs which she has shown literally zero interest in, or becoming a fleet commander, despite the fact that Carrot is a follower and not a leader. She was even following after fucking Chopper in WCI xD, and even recently Siciliian declared himself the leader of the minks in the dukes stead.
The most logical line would simply be that she joins the straw hats considering her entire character story. Everything else seems heavily influenced by bias and people who simply don't want her to join under any circumstances.
Giving what I've presented, can someone present a single alternative that given Carrot's character role, her lust for adventure, her bond with the straw hats, her fighting skills, her mentor's dying words...a single alternative that makes more sense than her... simply joining the crew...