They just kind of glossed over the whole plot to kill the king real quick there. Like, "we were gonna casually kill the human king to break the curse or something, but I guess we will just leave".
I know the witch in the little mermaid can just make up random conditions for her magic to work, but would it work with any king's blood, or just this specific king? Could we make someone king for a day and kill him? There's a lot of details left out here, haha.