Zoro is to the scabbards what Luffy was to Law in Dressrosa. Law failed to do the job properly and Luffy finished it. It will be the same in Zoro's case.
Kaido was injured by the likes of Kinemon and Kiku. At the same time, Kinemon shat his pants at the display of base Zoro shopping the golem down to pieces, saying that he personally would not take on Enma. And not only did the training with Enma further hone his Haki, Zoro still has powers up his sleeve like Asura, which is his mode equivalent to G4, where he basically triples his power. 9 blades with 3 being Enma, pumping his arms and upper body full of Haki. If that can't hurt Kaido while Kiku and Kinemon could, something's obviously wrong with Oda, lmao.
And power aside, as people mentioned, there is enough portrayal and hints.
And I mean, Kidd is going to fight Kaido with some metal scrap. Slamming Apoo with it didn't even knock him out, while Zoro one shotted him with one sword.