As a Zoro fan, it'd be awful to take a weakened, beaten Kaido over Zoro achieving his literal purpose in the story.
Shiryuu will be cool and I'm sure that would be a hype battle. But Mihawk has been established as Zoro's desired opponent since chapter 60~ or so. Any quick changes to this, without a proper build up between Shiryuu and Zoro, would be so empty beyond the initial grudge match factor of their battle.
And honestly, I don't think Zoro would be all that torn up about Mihawk dying. Sure, upset and all. But I don't think he'd be teary eyed over Mihawk dying in battle.