Tbh the Yamato vs Carrot Debate is really quite one sided imo.
Every straw hat who joined were main characters in a arc, most of the time it was in the arc they were introduced.
The only exceptions where oda strayed from this pattern of writing was for Robin and Jinbe.
Robin joined at the end of the Alabasta Arc and had her character arc done and ended in the Enies Lobby Arc.
Jinbe was introduced in the Impel Down Arc, had his character Arc in the Post Time Skip Fishman Island Arc, became a Straw Hat in the WCI Arc, and joined in the Wano Arc.
Carrot even now is still a side character, who was introduced all the way back in Zou and never became a main character in the Zou Arc, nor the WCI Arc, and with her having to share her fight against Perospero (a previous Arc's side character) with Wanda (a previous Arc's side character) now in the Wano Arc, it just doesn't spell Next Nakama to me.
With the way the Wano Arc has been going and the absence of Carrot however many chapters ago, Oda would need to squeeze in Carrot's writing, along with a multi chapter flashback into the Wano Arc- and i just don't see where Oda can squeeze this in anymore in a arc that is already filled with so many other important characters and important plot points, so that Carrot's multi chapter flashback can stand out and feel memorable and not forgettable. It also doesn't help that Carrot right now is currently unconscious and hasn't appeared in the manga for many chapters now.
I also don't see Oda postponing Carrot's Arc to another Arc post Wano, when Jinbe has already joined and officially become a member in the current Wano Arc. Jack, Perospero and the Beast Pirates, the mink's and Carrot's enemies, would also not be available in the arc after Wano.
If Carrot really is the better next Straw Hat candidate than Yamato, then Oda would've done Carrot's multiple chapter character Arc in WCI, where Carrot's Sulong transformation and Pedro's death was still fresh in everybody's mind. That was the apex and high point of Carrot's writing in the manga, and Oda didn't do it.
Even if Yamato wasn't introduced at the start of the Wano Arc, hell even if Yamato's character and backstory isn't completed in the Wano Arc- it would still be way better than Carrot's who hasn't done hers in the span of what is now 2 and a half arcs now.
If Carrot were to join instead of Yamato, Oda would still need to write Carrot's arc and her fleshed out backstory that is still missing from the manga, and a Post Wano Carrot Character Arc just isn't as compelling as a Yamato Wano War Arc involving Kaido, Big Mom and the other Supernovas.
Dunking on Yamato and creating all these 'artificial barriers' and obscure 'criteria' like the ridiculous Colour Pattern Theory or Yamato 'stay in Wano' Takeru Theory does nothing in improving Carrot's argument in terms of her writing, focus and characterization as a potential next Straw Hat, something that Carrot is sorely lacking in and needs right now. It just exposes how lacking of character focus and writing Carrot has had when you need to resort to using elements outside the actual manga to argue against another Straw hat candidate. Even worse is when the poorly thought out Yamato won't or can't join theories or arguments get debunked and disproven by the manga chapters themselves.