Because the final war will be extreme. Just by things we know, the battleforce of the WG consists of Imu + 5 gorosei + Akainu + 3 Admirals + X.
These are at least (!) 10 hard hitters, which are way above the most strawhats. I would expect Luffy to bring up a lot of people and Kaido + Yamato joining this war to bring down the government sounds logical for me. Remember, his strongest ability is to gather all people around him, even his enemies.
And Kaidos flashback so far fits that idea. He seems depressed since he gave up the idea of people able to change the world. Thats why he wanted to fight the strongest, he wanted to find joyboy. If he can accept now he found him, i can see him changing is point of view, gathering hope to see a different world, maybe changing his relationship to his daughter.