There's really nothing so complicated about it. When Luffy used it, Garp said he was BORN with it.
Ivankov said ITS in his blood.
Being born with something and the thing being related to blood is pretty much saying it's genetic. It's not something you choose to have. You either have it or you don't.
Crocodile having it will mean he was born with it, otherwise, he simply doesn't have it. It has nothing with being arrogant.
Arrogance is something that can be developed, yet Rayleigh has said you can't train to acquire it meaning... you can't influence possessing King's Haki, you can't Arrogance your way into it or try to be a edge-lord your way into acquiring Conqueror's, you either are born with it or not.
That's all I'll be saying.
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It is rare, we're just seeing all the people that have it.
There are billions of people in One Piece.
The Grand Line and new world is where all the strongest people in the world go to, so it's not really rare to see people with it only because we're at a location where there are lots of powerful people.
It's like going to a Zoo and seeing a Tiger (endangered species), there are only 5 thousand of them remaining. Just because you go to a Zoo and see 100 tigers doesn't mean Tiger's aren't rare. You're just in a location where they're concentrated.
The Grand Line and New World are places where CoC users are like Tigers, they're rare, but they're all concentrated in 1 area of the world.
And they're really only a handful of CoC users in the series, there are 22 known king haki users out of a population easily exceeding even a population of 8 billion given the OP world is larger than the the earth.
Out of potentially maybe even 20 billion people, only 22 known CoC users? That's not a lot. We just happen to be where all of them gather.