the problem is that some people here think that their candidates will join, just because they found something in common between their candidate and a SH member, even though that thing is unrelated to joining matters, and they tend to force these things for their candidates, which makes their explanation really stupid.
for example if Luffy told Zoro to help him, and said the same thing to their candidate, then they will say that their candidate must be joining, just because Luffy told him/her to help him, just like Zoro.
for me, what really matters is what the characters themselves say and want, what they have in common with SHs, and these common things should be related to joining matters, to SHs matters, not just some random things, that's why I think Yamato will join, because she wants to join, she said that she will join, she knows Luffy's dream just like the other SHs, and when Momonosuke called the SHs with their joining order in chapter 1056, he called her after Jinbe, which was a clear hint since Momo doesn't know the SHs joining order (Luffy, Zoro, Nami, Usopp, Sanji, Chopper, Robin, Franky, Brook, Jinbe, Yamato, that's what Momo said.)
so no matter how many times you try to deceive yourselves, it's clear that Yamato has highest possibility of joining, because she has a lot more things to be a SH than any other candidate.
Luffy is the protagonist, so, it's really about what he says.
Like, Luffy invited Gaimon, a man trapped in a treasure chest, to join his crew. And he was 100% serious.
Luffy invited Brook, a talking skeleton, to join his crew, without knowing really anything about him.
So, you need an invite, a dream that involves sailing around the world, and, as much as I hate to give this to C4N, a "shining Nakama moment".
Gaimon already had a dream that didn't align with Luffy's; he wanted to stay on the island with his weird animal buddies.
Brook had a dream, to recover his shadow and then return to Laboon, that originally didn't align with the Straw Hats, but, circumstances led to their goals being the same, so he joined after being invited more formally.
Momo's dream to become a great Shogun of Wano doesn't keep him from joining the Straw Hats, and he has an invite, and a SNM (Shining Nakama Moment) in stopping Onigashima from falling and killing... well, pretty much everyone. So, he can join, if Oden's journal/Momo's role as Shogun involves him going to Laugh Tale.
Kinemon's dream was to kill Kaido and help Momo rule as Shogun, but, he's never really had a shining moment, IMO, and his dream is connected to Momo, not the Straw Hats themselves, making him more like a Pedro. He won't actually join (I think Kinemon will die when Pluton is activated).
Vivi's dream was to protect and rule her kingdom. So, she couldn't sail with the Straw Hats. BUT, now that the WG is a direct enemy of Alabasta, Vivi will join the Straw Hats, who have declared war on the WG and Celestial Dragons multiple times by now. The only way Alabasta can be protected, is through Joy Boy/the Straw Hats. Vivi also has plenty of Shining Moments, from stopping the bomb in Alubarna, to fighting the Bananagator to try to save the crew. So, Vivi will join soon.
Yamato's dream was to fulfill Oden's Will, defeat Kaido, and open the borders of Wano so she could set sail to the sea. However, since Momo didn't have Zunesha open the borders at the end of the raid, Yamato still needs to fulfill Oden's will. Yamato will join, but only after Pluton is activated and the borders are open. Her shining moments were catching Luffy as he fell, holding back Kaido, and defending Momo and Shinobu from multiple enemies.
And then there's the mutherfucking problem child, the god damn rabbit.
Oda made Carrot a huge focus in Whole Cake, giving her a mentor death, a Roger tie-in, a tie-in to bringing about the Dawn, and having her interact with the crew regularly. By the end of Whole Cake, when you look back at Zou, Carrot had interacted heavily with the entire crew, including Jinbei. This is something neither Yamato, nor Vivi ever achieved.
Carrot also had many Shining Nakama moments, from trying to avenge her mentor, Pedro, to help the Straw Hats escape, to her conversation with Sanji, to her trap with Chopper against Brulee, to her super cool Sulong rampage that saved the Straw Hats from sure death.
SO WHERE'S THE FUCKING INVITE, ODA?!?!?!?
There's no way the Straw Hats never talked to Carrot about her future before leaving after they've sailed and fought together so much. And, guess what? We saw from Yamato that Oda has no problem holding shitty Wano Nakama flashbacks till later.
The most likely answer here is that Carrot already declined an invite to the crew, in order to rebuild Zou, the same way Vivi did. Once Zou is attacked by the WG, and Zunesha is killed, the Minks will migrate to Wano, and Carrot will be able to join.
We'll get a flashback of Carrot declining to join the next time we see Zou, most likely with Bepo swimming to the island with Law, since Bepo has a Vivre Card of Zou and Zou would be the closest island to Winners Island where the Heart Pirates took their big L.
Carrot's dream is to fulfill Pedro's Will, and Pedro's Will/dream was to sail with Roger, the Pirate King, to bring about the Dawn. So, we just need an invite, and Carrot to be forced to leave Zou like Vivi was forced to leave Alabasta (Carrot is the Vivi of the New World, a foreign royal connected to the Ancient Kingdom who was left behind to rule her kingdom).
If Oda actually sidelined Carrot being asked to join the crew for multiple volumes, though, he's a fucking madman, and I hope a dog scratches its ass all over his carpet for making me read C4N's thread-derailment-syndrome for another 6 months. STOP HOLDING BACK INFORMATION JUST TO DESTROY YOUR OWN FANBASE'S SANITY, GOD DAMN IT ODA.