I'm hoping this development is happening because the author realized that once Nanami's dad finds out Kaoru = Koari, he'll have less excuses to cross-dress, and thus the author had the class rep find out here so that she could goad Kaoru into doing it later.
(Though the author did already sort of blow the load on that with him cross-dressing the very first time Nanami visited his class, and even winning a popularity contest. Feels like the author might just act like that didn't happen, given the class rep's reaction.)