Being fascinated is one thing, being convinced that Luffy is the man that will become the pirate King and help you fullfill your purpose and be you life long friend is another.
Yamato as yet to understand why she would follow Luffy with her life. Right now, she is FAR from that point, Carrot on the other hand, not so much.
No it's not.
1. Yamato didn't decided to follow Luffy, she is not following him, what she is following right now is her desire to free Wano.
2. The reason why she DECIDED that she had a place on the Sunny was because Luffy was Ace' brother. There is no other reason until now in the story. Don't invent stuff.
We don't know that. Don't invent stuff
No. She was a supporting ennemy character. Her importance only came to light during the very end of whole cake. Her status gave you the illusion of importance (and Oda was counting on that). But in the fact, what Robin did was very little until the very end of the arc.
That makes her a savior, not a foundamental character of the arc. By that logic I could say that carrot saved the strawhat at the end of whole cake and is therefore important in the arc. (and don't even TRY to debate that point, I won't reply to BS more than necessary) And it would not be fair. Carrot was not THAT important in the arc.
On the other hand, you couled argue that Brook was.
Only you finds way to spin your own argumentation to avoid the realization of being proven wrong.
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Like I said, being fascinated is a thing and actually knowing why a character must follow another with their life is another. Completely different things.
No you can't replace Carrot. You would need to completely change the story to do that. Just like you would need to change the story to replace Robin.