Kaido’s true dream is not to become Joyboy or even Pirates King. He wants a glorious death, worthy of legends. That’s the first time Oda showed us Kaido, he expressed his wish to die. It was his introduction for a reason, Oda like his parallels. He will get his wish. He will die.
I believe his actual dream is to be defeated by Joyboy and get that glorious death he’s so desperate for. That’s why he’s at Wano. Oden and Toki knew about this prophecy. So did Roger and his crew. “They were too early”.
Kaido wants to become the reason a new Joyboy arises. Defeating the strongest creature in the world, and become a Legend worthy of the title as he goes down as the most notorious villain in the story, thereby gaining the fame and glory in death he wanted to justify his legacy.
His reasons of starting a war could also hinge on him wanting a new Joyboy to emerge. He probably knows more than Big Mom about the Legends as it stands as while she is only concerned about her Empire. Kaido has repeatedly shown interest in training/ capturing stronger enemies. All of which I believe is to find the famed unbreakable will of JOYBOY….
That’s what he’s waiting for. That’s why he was so upset when he beat Luffy the last time. He said, “ I guess you couldn’t be Joyboy either.” Maybe that’s why he wanted to go to Marineford. Because just like Whitebeard, Roger (and possibly World Government) he believed Ace to be the next Joyboy.
Lastly, he’s getting more excited when Luffy shows his strength and fighting spirit. He even wondered about how far Luffy could go, even to the levels of Roger, Rocks and Whitebeard.
Theory by AJ (https://www.reddit.com/user/ajibril33)