Thinking about kumite - for most of my karate career previous to my current iteration, kumite consisted of "mitts and pads on" followed by "hajime". There really wasn't much in the way of preparation or training for this and I think the idea was that through repetitious punching and "blocking" in the air you would become a good bout fighter. This is NOT the case.
At the AKA we train for specific circumstances and with kumite there are specific things we need to train for. For example drills need to target (amongst other things), eliciting a trained response, multiple attacks, targeting, footwork, rhythm and clearing.
Incidentally, this is very different to self defence which is closer, dirtier and likely includes things like multiple attackers, voice/noise, locking/breaking/throwing/falling etc.
Does your training note the difference and does your kumite concentrate on what it should?