@SeaOfHope:
Besides everything I just said?
The potential for Carrot to be a crewmate is absolutely open yo her, because she is a blank slate.
However, because she is a blank slate she offers nothing to suggest she would be either.
Consider that if her lacking backstory is an anomaly and a reason she could be a frontrunner, then let's analyze what this actually means. Let's take a look at other frontrunners that loosely fits this criteria.
Kinemon for example. Before we knew the revelation of him being Momo's retainer, who was he?
- Mysterious Samurai of Wano
- Interesting design
- Strong swordsman who uses 2 swords
- Can cut fire
- Has interesting fruit power, even fits 2-9 theory
- has Talking Farts gag
- Is looking for his friends and his son
- Travels with the strawhats through many arcs
Without any specific backstory, Kinemon would absolutely fit as a frontrunner and would also be considered an anomaly, because if we didn't know the revelation in Zou, all we have are guiding points telling us he could join the crew.
Now of course he has some obvious cons as a potential crewmate, like having a 'son' and being another Swordsman with little other role on the ship, but if we just regard the aspect of mystery kn the story, then the lack of a backstory would open up more potential only because there is nothing to discuss really. Prior to Zou, he and Momo could absolutely join the crew and go adventuring. The possibility continues now, but with much lower possibility due to Momo's importance to Wano in the story. And that is what ends up tying Kinemon to Wano really.
With Carrot, she doesn't have a backstory, so she has nothing tying her to Zou. At the same time, she's lacking a clear guideline like what Kinemon had (Find his friends) and that is what puts her in a very awkward spot in terms of character building. Even Pedro's words haven't been fully revealed by her acknowleding any deep understanding, so the breadcrumbs are there but as readers we should be aware that… there are breadcrumbs everywhere. She is literally a blank slate, and needs to be regarded as one. The intrigue you are feeling is normal, because we fill in the vlanks with what we interpret and would be interested to see confirmed. I believe Oda is intentionally seeding red herrings into the plot, and the mystery is the reason we are all able to discuss the potential crewmate, and not simply be unanimously saying 'that character obviously will/won't join because we know their backstory'