When he uses ashura against Kaido it immediately makes Kaido think that Zoro can use CoC
However Zoro doesn't seem to realize that ashura is using CoC. My explanation would be Zoro simply cant use powerful CoC twice in a short period since he hasn't mastered it, so he can't use it against King.
It is too powerful and not everyone can push Zoro to such a degree that he feels like he needs it.
There are two requirements for Asura:
1 - You are either very hard to cut like Pacifista and Kaido. (This is another proof that King has immunity.)
2 - You have an overwhelming combat style that can leave Santoryu Zoro no room to breathe like Kaku.
It would be too repetitive for drawing I guess (Zoro neither used that one which was used against Pica anymore, or Luffy didnt use a KKG for the second time and overall author likes to renew the moves, so many of them we don't see anymore or barely).
On the other hand, it's a technique used near the ground and Zoro finished King in the air. Finishing King in the ground would have let him there and he needed to be thrown away like Queen I guess.