To be frank I see no difference between Carrot and those mentioned.
Yamato is different given she hasn't been in the series very long
How so? Do I really need to explain why?
- Monet: Villain, zero connection to the crew. Zero instances where her character pointed to wanted to be associated with the strawhats.
- Perona: Villain, connection to Zoro but still massive dedication to Moria. Read the above.
- Rebecca: Arc princess, was painted as nothing more than that. Zero desire to be a pirate. Zero desire to adventure.
- Pudding: Essentially the "Arc Princess". Aside from a connection to Sanji, zero merit for her actually joining the crew. Zero actual decent interactions with the crew. Nothing pointed to her actually wanting to leave WCI.
- Ulti: Villain, zero connection to the crew (so far)
- Momo: "Arc Prince". Zero desire to be a pirate. Zero desire to follow in his fathers footsteps and "adventure".
- Law: Is his own captain, shows zero interest in subjugating to Luffy outside of an alliance. That's the point of his character, to be Luffy's first true pirate Ally. Kid is also going in that direction. Bege already fell in that direction.
- Kinemon: To be honest, he's the closest out of the above to have some sort personal connection to the crew. But, Kinemon has had zero hints to wanting to go on adventures. Has a desire to serve only his countries problems (like Momo). Has a desire to return to his wife.
Adventuring is pretty much the lifeblood of Carrot's admittedly "small" character. Aside from Luffy, she has interacted with much of the crew, more so than any other character above has at this point. She experienced a tragedy in real time with Pedro, who told her that she will eventually realize how important the strawhats are to changing the world, who's dream was to travel with the PK, who essentially passed on his will to her almost entirely. She's the only Mink that received exclusive focus with the strwhats. She essentially receives more focus than the 2 Mink Kings at this point, save for certain points in Wano so far.
Then you have Yamato, who point blank told Luffy he/she wanted to leave with him, along with being exclusively with Luffy the last 4 chapters, connection to Ace, hinted tragedy directly related to her father. Not much else there considering she needs needs more chapter presence still.
How is it hard to see the difference between these 2 and literally every other side character in the series outside of Vivi? Its not about patterns, its about how Oda writes these characters, and so far these 2 characters have far more interest in adventuring (with the strawhats specifically), wacky personalities, moderately unique fighting styles, and have presence unlike the rest.
Come on Garp, there is a huge reason why Carrot and Yamato are almost exclusively discussed here. Its because everyone sees the same merits more than any other character. Its also why point of contention is so strong on opposing sides, and why the arguments are much more heated. Nobody here argues more about Perona or Monet joining than Carrot and (so far) Yamato, because most people understand that Perona/Monet had almost had no motivations in joining.