Yep, I agree no, HC is as knowledgeable on both side of the ball though I think Belichick is probably the closest to that, however KK is pretty distant from the defense in any way shape or form. I think most HCs have at least a reasonable grasp on what is happening on the side of the ball they are less familiar with and probably have some input into some decisions made on that side. I suspect KK doesn't dwell or spend much time at all on the defense preferring to let Vance handle 90-95% of the load with his staff while KK focuses on the offense. It would not even surprise me if KKs interaction with the defensive players is not nearly as intense, close, personal, or whatever adjective you would like to use here as it is with the offensive players.
I guess it would make for some interesting viewing to see how much interaction KK has with players from each side of the ball during warmups and practices and during the games. What is his demeanor during games when the defense is on the field? Is he focused on how the defense is playing or is he more involved with the offense (head buried in the play book) while the defense is out there? One would have to go re-watch some games to see.
My feeling and it's a gut feeling not based on anything I can point at is KK seldom really knows how well or how poorly the defense is playing because his emphasis and focus is more on the offense than the performance of the entire team. I would prefer my HC to have a pulse on all phases of the game and how each are performing and be prepared to make decisions based on those observations.