Kicking the ship off the waterfall doesn't make King > Katakuri. Kaido himself said they would not be prepared for a war with the BMPs. BM wanted King to join, cuz he is one of the 3 races her nation still lacks. Powerwise, Katakuri has portrayal over King. As the perfect undefeated human who has FS, something that, according to Rayleigh, only some even among the most powerful have.