Honestly, this really fucking bothered me, I expected Kaido to snap and mourn for him, especially given how close they were in their flashbacks and him being Kaido's right hand. King obviously really respected and admired Kaido and paralleled Zoro's respect and admiration for Luffy much in the same way too.
I would have this be the prerogative to truly take that demonic silhouette appearance and strike Luffy down with that blow that "killed him" too, Kaido unleashing his wrath of losing King on the captain of the person responsible for him losing King, potentially permanently/in death too.
There was that great dynamic of Zoro and King, that was akin to Luffy and Katakuri too even. King even made his ultimate attack a literally huge tribute towards Kaido and then some!
I may have to write Kaido reacting to Kings defeat in the way he should have imo. I'm so frustrated about that lol. He legit seemed to care more for Jack than he did for King lol. Meanwhile I wouldn't have minded if Kaido made a sarcastic comment on Queen being defeated, remarking how foolish/arrogant and unreliable he can be lol or just being kinda sour about it anyway.