I think how this is going to go down, is Kaido will start rambling about Luffy becoming Joy Boy, and Luffy will reject the title, insisting he’s just Luffy.
Similar to how Luffy rejected the ruler role over the Grand Fleet, throwing a wrench their vision of what it means to be King of the Pirates, Luffy will throw a wrench in Kaido’s idea of the Joy Boy prophecy, as well as the notion that someone must turn into Joy Boy – as Luffy isn’t changing to fit into a role, he simply is the right person for that role by nature of who he is. The title is superfluous. Luffy has already shown time and time again that he doesn’t care about the titles themselves or prophecies. He’s too straight-forward and self-interested for things like that.
And Yamato seeing this declaration, would then recognize that she doesn’t have to ~be~ Oden in order to become her ideal self. Yamato can just be Yamato.
From this perspective, Kaido (if he’s trying to become Joy Boy) is falling into the same trap as Yamato. Trying to become something he just isn’t, trying to cast himself into a role, rather than simply being himself.
He’s clearly a different person from the young, bright-eyed, cheery Kaido we’ve seen. Maybe this is the reason he strayed so far off course and became a shell of his former self.