RIP King can beat Katakuri.
He needs to fight without his enhanced durability if he wants any chance of avoiding Katakuri's attacks, and that would only get him so far.
Kuri has Mogura, Awakening, next tier Hardening, Future Sight.
King has dura-negation that nerfs his speed.
Chadakuri >
Base King fought hybrid Marco .
Such Marco fight Kizaru so unlikely King to be overwhelmed even more when we remember base Luffy was already evading Katakuri attacks.
Additionally he doesn't to avoid attacks that will do no damage.
Katakuri doesn't even have aCoA just good koka and mogura is irrelevant due King being able to use against Katakuri in a explosion.
Katakuri simply lacks what is needed to push King into his speed mode which is AP.
It's curious you know....
to beat Katakuri Luffy needed to be faster and to beat King Zoro had to tap into aCoC(AP)
Both abilities that not anyone can get.