The issue with Zoro killing Kaido is that he has really been presented as unimportant in the last few chapters and spotlight has been put on Luffy, Law and Kidd.
Oda hasn't created any personal conflict between Kaido and Zoro, he hasn't created any family ties with Zoro and Wano Kuni where he could have written revenge archetype with Zoro killing Kaido.
Before Odens flashback there was one plot point supporting Zoro damaging or even killing Kaido and that was Enma supposedly being the only sword to damage Kaido but that was quickly proven false in the flash back.
At this point all we have is loose parallels of Ryuma slaying the dragon to save Wano Kuni from it but issue with that is Zoro has even lost Shushui and so far Oda hasn't put any focus of Ryuma besides those words from Gyukimaru
And now we are in the starting point of the war, the strawhats are in Onigashima and next step is the plan coming into fruition.
The only plus point in Zoro killing Kaido is his sub plot with Hiyori but even in that sub plot Orochi was portrayed as main antagonist and not Kaido.
With all that why would Zoro kill Kaido?