While I understand your argument, I don't think it holds up well to scrutiny. Carrot can face a new challenge in a single chapter (or half a chapter) and not have it be a major deal. She can drop in to rescue a weakened strawhat in the end of a chapter, thus proving herself, and then not have the fight shown on panel, and it would fulifil the setup from perospero. That would be a super anticlimactic and dissapointing way to do it, but I was hoping for her to get a big 1v1 against peros, and that didn't happen either.
As far as the giants, sure it's possible she could be involved in Elbaf, especially if Big Mom is there (although that looks doubtful now), but this is based on a single line of dialougue that was said in the middle of an important conversation about other things. It's not like Ussop's comments about the giants. It could easily have simply been a flavor thing, continuing to showcase Carrot's sense of wonder. I bet she would have said the same thing about mermaids if they were mentioned.
This all seems like speculation. Could it happen? Sure, it's possible. But it's not a strong enough basis to form an argument on imo.
As far as thriller bark, I disagree. The entire reason they went there was to recover Brook's shadow so he could join the crew, and the moments he was present were some of the most important parts of the arc. He may not have been a constant presence, but he was definitely important.
That's why it's still a little theory. There is too few element to be sure. The only thing I'm sure of, is that Carrot needs at one point or another prove to herself that the words spoken to Perospero are wrong. Now it could take multiple form, and i'm not even sure that Carrot really needs an ennemy.
I did not say that Brook was not important, just that Brook was not the center of the arc like Robin or Nami were during there time. He might have been the trigger, but that's all. Only the last chapters were really brook centered.
That's why I don't think Carrot's really needs to be the center of attention in any arc. But she will have to be the center of attention for at least one chapter or two. And that can be done in so many way it's impossible to really predict how.
Now.. Carrot only needs one things: the will to sneak aboard the Sunny (and even that might already be there). Really, that's all we need right now. The rest might come after, it doesn't matter. Carrot won't be a strawhat yet, but her presence will seal the last place unless she find her true purpose outside Wano, Zou or the Strawhats somehwere else down the line, which would be very unlikely.
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Another thing to note is that...
If Yamato does join the group, she will have lost her "time to shine". Narratively, Yamato is put under such a light that you can be sure that EVEN IF Yamato does jooin the group, she will not have a major role after that. Her time is now. This is proven by her flashbacks and the way she is portrayed as the heroin of the arc.
Narratively, it wouldn't make much sence to have Yamato repeat this role in the next arc. So at best, she will be like Sanji here in Wano.. an important protagonist, but not one that can steer the story.
(I hope, you understand this point)
On the other hand.. Carrot does not have this problem, Carrot didn't shined that much in whole cake, and didn't shined at all in Wano.. so it leave the possibility of Carrot being a HUGE protagonist in the following arc, completely open.
And it would make perfect sence. If Carrot joins, this will be as a stowaway, the next arc will therefore act as a trial.
Now.. I will enter complete hypothesis territory here but bare with me:
I would love to see the dynamic between Usopp and Carrot during a potential Elbaf arc.
Why ?
We know that Carrot and Usopp are going along pretty well because of the two interactions they had on Zou.. Now, if we are on Elbaf next.. we will surely focus on the Wonder of Usopp on the glory of the Giant, this would resonnate pretty well with how Carrot will see the world at that time..
Two mugiwara, wanting to be stronger warriors without fear for the world beyond their reach. I'm just sayin.. it could be cool.