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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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.
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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.