Law doesn't need CoC. CoC is like adding a strawberry on top of a wedding cake. His DF abilities are so powerful and lethal that it's like he's already using ACoC ver 2. His ope can do literally anything, killing a HK is not out of realm for him, as the one whose powers granted Imu immortality to begin with
The only reason to have it would be for the love of the game, to glaze him. Check off the list of confirmed conqueror's since Law is clearly one. And to keep zoro fans in check
Kikoku revealed as a country-buster cursed sword is a FAR more valuable lore drop than CoA 2.0