@KazumaLee94
Well whenever Izumi tries do to do something o his own or tries to act cool, the universe punishes him and Shikimori needs to rescue him. It seems there is nothing he can do.
Though the chapters that introduce Kamiya show he can exist on his own even influence other characters, then again he probably wouldn't be able to do that if not Shikimori's influence on him.
The Izumi-less chapters work as a way to develop the side characters/ their relationships with Shikimori, so mentioning Izumi in them wouldn't necessarily make sense.