What are you even yapping? Shanks and Whitebeard showed no interest in the one piece at the time.. why would they want to take over other territories?
It doesn't matter if they talked. Big Mom said that she would've destroyed Kaido if she got Elbaf's alliance and mentioned him in the same breath as Shanks/Whitebeard who she had 0 cordial relationship with. They still wanted to be the one on top, no matter how competitive it was.
This has to be the final band of cope
ignore Kaido's words and takes yours!
Anyways, your King example works against you in this case. Kaido was so confident that he'd pull up to Marineford and face off a Yonko crew, a Yonko, all the Yonko crew's allies, tens of thousands of marines, 3 admirals, 7 warlords, multiple vice admirals, Garp and the fleet admiral with
just King but was worried about a war with Linlin + friends when he had
King + all of Queen, Jack, Tobiroppo and HIS ENTIRE ARMY. This just shows how strong the BMP are and Kaido knows that better than anybody. He was infinitely less confident vs BM and 8 commanders than he was of... everyone in the biggest war in modern piracy history.