Kaido wants Joy Boy to exist.
IMO, Kaido went to Fish-Man Island and talked to Shyarly. The timing fits: Shyarly was 3 at that time, and she was already making prophecies by then, canonically.
Shyarly told Kaido he wasn't Joy Boy, but Joy Boy would be the one to defeat him.
The Kaido from King's flashback has a straight up Roger/Luffy smile: Kaido BELEIVED he was Joy Boy. Then, found out he wasn't.
Kaido realizes Ace is Roger's kid, and believes him to be Joy Boy.
There's one card missing from Kaido's Crew/Deck: the Ace.
Kaido respected the people who challenged him, Kaido wouldn't want to kill Ace. Kaido wanted Kidd and Luffy to both join his crew, and even had Queen run the Sumo Inferno to break Luffy's will so he'd join. Queen told Luffy that at any point, he could join Kaido's crew and stop fighting.
Kaido wants Joy Boy to be real: Roger's son LITERALLY SHOWS UP TO FIGHT HIM, and before Kaido can, Ace gets killed.
The hilarious part of this is that if I'm right, Kaido HAAAAAAAAAAAAAAAAAAAAAAATES AKAINU
The money I don't have that I would pay if I did
To see Hybrid Flame Dragon Torch Kaido vs Awakened Akainu (plz Wano Act 4 plz)
Kaido wanted to create a world war. Kaido dislike Newgate's pacifist approach, IMO. But, Ace? Ace was a hot-head.
Kaido knew Newgate was on his last legs: Kaido wanted to steal Ace for himself, like he tried to get Luffy and Kidd into his crew.
Kaido wanted Ace the same reason the WG wanted to kill him:
They both thought Ace would be Joy Boy
But, nope, it's this dingus:
Kaido spent all this time telling Linlin he'd kill her if she came to Wano.
Queen dragged Linlin to Kaido in chains...
And he freed her...
To fight her...
And a few hours later they were drinking together and making a Yonkou Alliance
Like fucking shit Kaido would try to kill Newgate, he's his Nakama
Kaido went to Marineford to fuck up the Marines, why in the fuck would he choose to fight his former Nakama, Newgate, when Kaido despises the WG/CDs?
Why in the fuck would Kaido want to kill Ace?