Has anyone given an actual reason for why they think Carrot isn’t gonna accept the offer and just totally betray her entire nation, or is it just anti-Yamato fatigue finally reaching its natural conclusion??
Because it's not an offer. They didn't ask. They told her, "You're going to be ruler," and they won't hear a word against it. Whether she goes through with it or not, she has to be free to choose. Just like Yamato has to be free to decide what he wants to do for himself. Whatever happens to both of them, their free will should be respected.
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Y’all just remember:
Kaido forcing Yamato into being shogun = “She’s gonna stay and protect Wano!!”
Carrot being asked by Neko and Inu to lead Zou = “She’s gonna leave with Luffy!!”
MAKE IT MAKE SENSE


I do feel there's a bit of nuance to examine here.
In Yamato's case, I don't think anyone wanted him to follow Kaido's command to stay in Wano as his shogun lackey. Once Kaido was gone, Yamato would be free to do whatever he wants. That includes leaving as well as staying, this time by choice.
There is that interesting bit in the previous chapter where Momo refuses to let Yamato help fight and basically tells him to just leave, that he's free now. Yes, Yamato is now free. And he's just as free to leave with Luffy as he is to see past Momo's bravado, into his realization that people are leaving him behind, and chose to stay.
Now Carrot is being, I'm not going to say forced, but pressured into being a ruler. If she is going to take the job, we would want it to be because she actually wants it, that it really would be Pedro's will that she do it. But she knows he died for something bigger, that what he wanted couldn't just be found on Zou. His words to keep moving forward rang out to her twice this battle, the second time right before Perospero told her to run back home. And now she's being told that's exactly what she should do because Pedro would have wanted it. It simply doesn't add up to me.
I feel there's a subtle but very real difference between choosing to stay because someone hopes you won't go and staying because someone expects you to stay. Momo and Yamato had been building a bond for the entire time they were together. We always knew if Yamato decided to stay, it would be because of Momo, not Kaido, and that it would be by choice, not because he's Momo's servant or a duty as some guardian of Wano bound by a fruit. If Carrot stays, it shouldn't be because anyone tells her it's her duty. There has to be someone that compells her to choose to return to Zou, and the closest that would be is Pedro, whose will she inherited. However, I will never believe that his will meant for her to go back.