All Yonko are about equal, hence the deadlock.
Just because Kaido is stronger than Shanks Doesnt mean he can win easily, its an extreme diff fight against Shanks alone.
So even if Kaido was there with his whole crew, the fight would last days and then his crew would be too banged up ( or he would’ve even lose as i think RHP crew> BP) to go to MF , and the war would be over by then already.
So there was no point.
And if they fought anyways, he would open himself up for an attack from BB or BM or Marines.
Its a lose lose situation all around.