The main purpose of a CoC is to point to it when you want to ban someone. It's an accountability sink - instead of saying you want to ban someone, you say you have to ban them because they violated the written rules. The rules, of course, must be written vaguely enough that anyone you might want to ban is violating at least one. It's okay if people you don't want to ban also violate them, because you won't bring it up.

It can also be used as an accountability sink in cases where someone clearly should be banned but you don't have enough courage to say you are banning them because you think they should be. In this case you can also point to the rules. However, if the person who should be banned is sneaky enough, he didn't break any of them. You ban him anyway.