Kat only got CoC but Oda wanted the arc villain to look cool, not because it had any deep meaning behind it.
Yamato is also in the same boat having CoC just because her daddy has it btw, the point is you don't need a deep reasoning to be a Conqueror and looking for one is futile. If Scopper Gaban the #3 of the Pirate King can have it, so can Law who is very much going to be relevant going into endgame lol.
If Oda is going to have numerous characters unlock CoC into the endgame, he needs to retcon the logic behind CoC.
Because it was introduced as a power you are born with. Luffy got it pre skip when he was only 17 in his first year of piracy. Ace and Doffy both awakened it as children.
Now Zoro got it out of the blue, Sanji will probably get it, and so could a host of other characters.
Oda needs to drop the retcon that no, actually you don’t need to be born with it, you can in fact unlock it later in life. Else this is going to get really stupid.