The one thing that helps Kurumi becoming so likable is that KnT does not have purely antagonistic characters... at all, and many shoujo series have this agenda.
However I don't think a "Kurumi-show" could work on its own. She is this poor, likable character
because she is the "rejected side character" but then again she's also really pushy and doesn't flinch from using dirty tricks and deception. As a main girl this would be too much out of genre conventions, especially when looking at the target audience.
Sawako's strong point obviously is that she is special within these conventions.
On a side note, I really had to laugh at the flashback about misunderstandings being resolved by talking to each other
