This I don't understand. How can you recognise that Oden's flaw was doing things on his own, yet also believe Momo is going to develop into someone that does things on his own?
Yep. She was working alongside him and guiding him. Luffy can't stay with Momo forever, and so the role he played for Momo has been transferred over to Yamao. These last couple chapters were essentially the passing of the torch.
Passing of the dragon if you will. But Luffy can't stay with Momo forever. He's got his own journey. That's why it would work for someone like Yamao who hasn't begun her journey yet, to do so with Momo the son and successor of the man she admired. Adult Momo seemingly looks just like his father. What would be a better dream come true for Yamao than to sail around and adventure alongside "Oden"?
We've already seen that she can teach him how a shogun should act.
Oda's already shown her unknowingly demonstrating to Momo precisely that. Not the traditional idea of a shogun, but the sort of man Oden was. She's someone that can talk to him like an equal. She doesn't do or the whole "lord Monosuke" song and dance or treat him like glass. It's as Kin emon said back at Zou about Luffy:
When you take into account her strength, her knowledge about Momo's destiny and powers, her personality + dynamic with him, guardian of Wano devil fruit, then she's literally the perfect person to accompany him. That's not even including how much thematic sense it makes and what it would mean for the citizens of Wano and Yamao's backstory. The signs are honestly absolutely overwhelming.