It's just way to far fetched to believe that that Asura is AdCoC that Zoro had no clue even existed.
Oh shait.. ig i didnt clarify but i don't agree with the notion that it Advance Coc.. i believe its some sort of derivative of Coc.. but with the possibility that Zoro's spirit was soo overwhelming that kaido called it coc.. or that zoro doesn't knie the basics of Coc so he can't force it at will hence the area of influence ashura has is limited but that wouldn't explain why law didn't mention what Kaido did
.. Ashura is an oddity that must be covered honestly.. i share some of the doubts you do like why didn't Mihawk notice his Coc qualities and train him with it and hence make him stronger... or is it that zoro never pulled ashura against mihawk.. its astretch
And the problem with the desperate bloom of haki in this case is that it wasn't pointed out to be bloomed like it was in luffy's case..
In the case of Breath of all things.. oda took time to emphasize the state zoro was in and what he was feeling but here its FLIPIN AMBIGUOUS... with just Kaido calling out for zoro's coc.... it can be that just like luffy he didn't sense it at first hut zoro has been seen reacting to Luffy's Coc just like sanji...the only convenient answer would be that zoro never used ashura against Mihawk or never use it hence he doesn't know what it actually is... and Ashura is his last ditch attack a finisher something like San zen sakai.. so i doubt he'll use it often.
But this technique obeys a reliable definition of Coc... lets leave it to oda to cover thid mess