Katakuri hides his face for the sake of his siblings, he literally said in the flashbacks he doesn't care, he will just beat anyone if they laugh about it. Then they took avenge from his siblings, after that he decides to hide his face.
Kid also kills people when they laugh to his dreams, so that's basically the same thing. As well as Ace does the same when they talk bad about Whitebeard, or when they insulted him due to being Roger's son. They all have CoC Haki.