There is no problem, per say, with Zoro killing Kaido.
The issues lies with how Oda has treated killing within the story, and the fact that it has been nonexistent within the Straw Hats for 20+ years, and 1000+ chapters. To go from that, to all of a sudden turning one of the Straw Hats into a murderer at the drop of a dime, with nothing to even properly justify it, would be horrible writing. Kaido is no different than any other villain in the story, with some being even arguably worse than him in terms of how they made people suffer. For Oda to justify having this man absolutely need to die, he'd have to break the mold and take Kaido to a whole different level of evil, and we are way beyond that point.