Its funny how you use the case of misdirection to discredit Yamato to favour Carrot, when its actually the reverse.
You talk about Yamato appearing out of nowhere asking to join is the Red Herring, but you don't talk about the Red Herring that has existed for the longest time, and that's Carrot.
Carrot has been the 'potential straw hat' for the longest time, yet she has had little to no developments necessary for a Straw Hat in the timespan and arcs she's been with them. No in-depth flashback and backstory, no real conversation or bonding with Luffy (biting Luffy's ears and crying in his arms don't count), and most importantly of all, Carrot has never had a arc where she was the main character, despite how many arcs she's been in.
Every Straw hat who joined had a arc dedicated to them where they were the main character and where their struggles were resolved by Luffy, Luffy defeated the arcs main villain who they couldn't defeat themselves. Carrot has none of this going for her, but Yamato has-Yamato's biggest obstacle of leaving Wano and adventuring the world is Kaido, the same Kaido that is the main villain that Luffy wants to take down the most.
Breaking a potential Straw Hat candidate from the villain's captive hold and giving them freedom (
Nami, Robin, Brook, Zoro etc) or the burden of responsibility that chains and binds them (
Jinbe, Sanji, Franky, Chopper, Ussop) is how the bond between a potential Straw Hat and Luffy is created and sealed in stone. It all resolves around the theme of Luffy giving them
freedom, either
freedom from their captors, or
freedom to pursue their dreams and ambitions. In return, the straw hats join Luffy's crew as gratitude for Luffy's help for either breaking them out from their captivity, or their inability to pursue their dreams.
All Straw Hats who joined felled in either one of the two categories. Yamato fits into the
Breaking a potential Straw Hat candidate from the villain's captive hold and giving them freedom Category along with Nami, Robin, Brook and Zoro. Carrot fits in neither.
Carrot neither has a villian that is holding her captive, nor a burden that is holding her back from pursuing her dreams (she freely snuck onto the Sunny so easily). So you can see that Carrot just doesn't have the necessary circumstance or backstory to make her bonding with Luffy a compelling one, biting his ears and crying for Pedro don't count.
Yamato's sudden introduction doesn't make her a Red Herring, it actually makes Carrot the Red Herring. If Yamato was the Red Herring, who is she the Red Herring for?? Carrot is actually the Red Herring for Yamato.
Its like the callback to Vivi and Robin, Vivi joined the Straw Hats adventures so easily, yet she still couldn't join the crew for real at the end of Alabasta, Robin meanwhile did. And just Like Yamato, both Robin and Nami were subordinates to Luffy's previous enemies Arlong and Crocodile, just like Yamato is the child of Kaido. Carrot doesn't fit this pattern.
Adding Carrot to the story while also her snucking on the ship, is Oda's intentional doing to serve 2 purposes, and none of them have to do with Carrot joining the crew:
1. Carrot is used as the Red Herring, or bait and misdirection so to speak for the totally unexpected introduction of the real Straw Hat Yamato in the Wano Arc.
2. Carrot is introduced and made to go along with Luffy and half the Straw Hats to WCI as the eye witness to live to tell the tales of the Straw Hats long into the future, in this sense Carrot mirrors the roles that both Inuarashi and Nekomamushi played in sailing with the Pirate King Gol D Roger as Oden's retainers. Neither two went to Laugh Tale, and i don't think Carrot will either.
It's also ironic how you have to resort to manga panels that are misleading to what you are talking about, that's your intentional misdirection. Brook's real focus panel isn't when he first met Luffy, Nami and Sanji. Its when Brook asks Luffy if he can join the crew when Luffy's was lying on the piano that Brook played Bink's Sake at the party after defeating Moria in Chapter 489. It was set up as a 1 one 1 conversation, a conversation that Yamato and Luffy also had together and alone in the attic of Kaido's castle in chapter 984.
Now speaking of which, where is Carrot's one on one talk with Luffy about her wanting to join the crew? All right, she doesn't have one.
