Something that Luffy always did was kill a person's dream instead of killing the actual person, and Zoro has in the past said Luffy was too soft as a captain.
I was thinking if it happened that way Luffy would defeat Kaido, and then he would try to give him a chance to redeem himself later, and Zoro would tell him not to do it and just kill him, and then when Kaido tried to pull a Frieza on Luffy, Zoro would finish him.
The issue with that thinking though is that it would..
1) it would mean Zoro would be further convinced that Luffy is unfit as a captain
2) it would mean Zoro disobeyed Luffy.
It might've been cool, because then we would've gotten the whole "a new legend was born, the story of a man who killed an Eastern Dragon" and a parallel to Ryuma, but ya that specific situation would've been similar to the whole Frieza thing.
If Kaido launched one last desperate Bolo Breath while Luffy was walking away and Zoro yelled "You fool!!" (referring to Luffy) as he cuts his head off.