This actually brings up a very valid point. Not only does Zoro killing Kaido place his name on a plateau across the World above that of his own Captain, but it also eclipses any future news regarding him defeating Mihawk. Kaido is regarded by the people of the Verse as the World's Strongest Creature. It's not a title in a box to the people of the World of One Piece, it's the general consensus. With CP-0 there, it's no longer a legend of slaying a Dragon contained in Wano. It turns it into a Legend of killing The World's Strongest Creature, The Yonko Kaido, across the entire World. ZKK literally can not happen for the sake of Zoro's dream.
Luffy defeated Doflamingo & yet both Luffy & Law got same Credit for it & even same Bounty
Not to mention that Luffy already have a Bounty & Fame much higher than Zoro's
So Zoro slaying Kaido will help him catch up only
Luffy will still be credited for Kaido's Defeat too
Also with Fall of Kaido, Recent Removal of Shichibukai, Teach & Shanks making a Move, Dragon & WG Clash ... etc
It's obvious that the Stakes for Next Big Arc (Which is Final War) will be much Higher than simply Defeating a Yonko
Zoro defeating Mihawk was never said that it's gonna be Biggest News in Zoro's Life
It's a Battle for a Title, not a Battle with World Tilting Stakes & Consequences
Zoro proving himself as a Top Tier in Final War & help destroy WG & System of Yonko would already make people consider him among the Best in the World & a Legendary Name alongside Luffy, just like Rayleigh is said to have Legends & Myths written about him for simply being Roger's Right Hand Man (Now imagine Luffy & Zoro who are gonna do more than just find One Piece)
And it actually makes sense that when Zoro fights Mihawk for the Title, he is already considered a Candidate for the Title by most people & the whole world wants to see them fight.
It's better than writing on the News: "A certain Supernova managed to defeat Greatest Swordsman & claim his Title" !!
That is so lackluster & doesn't make sense, it doesn't Hype Zoro at all, it simply Dehypes Mihawk for the Public
So Zoro needs to first make a name for himself before facing Mihawk & he needs to do that by proving himself against Yonko & WG.
And this is something "Canon" as Shanks also told Luffy same exact words
Shanks refused to fight or even meet Luffy until the latter proves himself & reach certain level of Fame & Power.
Actually even after Luffy became World Famous, invaded Three Biggest Islands of WG, defeated some Shichibukai & ruined Big Mom's Territory & reached a Bounty above 1 billion, Shanks says "We will meet soon"
So Shanks is waiting for even more than that, that's so crazy
Same thing applies for Zoro, otherwise what are they waiting to fight again?
Obviously Mihawk told him to first help Luffy fulfill his Dream & become a Great Pirate & then they can Fight
Kaido will be known as the guy defeated by alliance of Supernova & Samurai
And WG always credit the Leaders & most notable members of the Alliance, not who delivered the final attack & who fought better.
They don't have such info & they don't really use it to judge danger of People
Achievements > Feats in "News & Fame" World