Ace came to Onigashima to fight Kaido but Kaido wasn’t there. So he fought Yamato and tied with her. He broke Kaido’s dragon statue as well. Maybe Kaido took this as a sign. Maybe Ace was Joy Boy. So he didn’t want Ace to die before he could fight him. But he never made it to Marineford because Shanks intercepted him.
I think Shanks convinced Kaido that Ace wasn’t Joy Boy. Which is why Kaido went away. This could add a new wrinkle to Shanks’ character as well.
2 years later, Kaido had grown tired of waiting. He has also heard of this now infamous “Worst Generation” of Pirates. Maybe Joy Boy is one of them. So when he received Intel from Apoo that Kid, Killer and Hawkins were there, he personally dropped in on them, to check whether Joy Boy was one of them.
Think about it. Why did Kaido go there personally? Why not send King and Queen? They could’ve handled it. He sent Jack (who has no named attacks) for something as important as taking back his most important business partner Doflamingo, but he went personally to capture a few Rookies? Why? I believe it was because he wanted to find Joy Boy. But he realized none of them had what it took.
When Big Mom told Kaido she wanted to kill Luffy, he objected. One of the main reasons I believe is because he wants to meet Luffy. He wants to see if Luffy was Joy Boy. And he is still interested in Luffy because out of all the people who have gone head to head with him 1v1, only Luffy was actively fighting for his friends and to free Wano. Not for clout, not for personal vengeance, but for freedom.
So overall, I think Kaido wanted to be Joy Boy but couldn’t. So he put himself in Joy Boy’s path to see why he couldn’t be Joy Boy and to maybe even die by his hands or because of him.
*Theory by OkUnderstanding3669