I really hadn't considerd that many of the characters might not have an overarching purpose. I was only thinking that I couldn't get behind any of the characters. Maybe I've been looking at the whole series sort of one dimensionally. I'll try reading the next book with that in mind and maybe I'll have a different opinion.
That said, I think maybe Martin tried to add in good sides to a few characters a bit too late. By book 2 you couldn't make Tyrion or Jaime into good characters. Once Jaime threw Bran off the balcony I don't care how many Brienne's he saved, he's still a bastard. And Tyrion, he's killed, tortured, and betrayed his way through the entire series. He's an interesting character, but not one I could see anyone getting behind. Would you really be interested in seeing him King? Or anything really?
I don't know there must be some reason I keep reading his books but the lack of a decent character to root for definitely pushes this series into my second tier of fantasy novels. Like I said, I can get behind an evil hero but it has to be more like Glen Cook's Black Company. Sure they're evil mercenaries but at least they're loyal to each other. I don't think the same can be said of any of Martin's characters.