The kingdom war is the sideshow, it is repeatedly stated (most recently by the maester at the wall) that the war is distracting from the real threat if the walkers and approaching winter. That's how the whole show started!
Danny's war is also a key part of the kingdom struggle as that is ultimately what she wants, the 7 kingdoms so you can't ignore her and then introduce a huge army at a later date. Plus it's obvious the dragons will be a key part of any war against the winter.
I didn't mean in terms of the plot - I've read the books. I meant in terms of what makes the story so good. The Wall stuff is just Zombies on Ice, and Danaerys is a badly imagined character who oscillates from hormonal teenager to grand dame for reasons far more related to the plot than to the character. It would have made far more sense to not even start the Essos stuff until book three or so, so that it actually moved a bit. What elevates the series is the character-driven stuff, which is almost all related to the War. If you took out the War of the Five Kings the series would be unreadable. If you removed Essos and the North it would be a sensible length, much better, and probably complete by now.