When each book is this long (heck, the series is huge) that there is a tendency to pick and choose... like at a salad bar. You can (and should) go read your favorite passages and chapters for enjoyment. (This is how I find quotes and trivia for our games here.) But if you only do that, I think your ability to relate certain characters, actions, and themes together will become limited.
When I fist picked up AGOT, ACOK, and ASOS, I read each of them in twenty-four hours and then I immediately reread each one. But with AFFC, I waited a day and then slowly reread it. And I took four days to read ADWD and then I waited six weeks to reread it.
I was caught up by AGOT and I loved discovering GRRM's world. But by AFFC and ADWD, the story was not going exactly the way I expected. Maybe that's because I had so much time to think about the characters and the plots. I admit that I've been disappointed (during my first read) with some of the directions that each character takes. But the rereads have been more fulfilling than the rereads of the first three books.
For example, Brienne's POV has mayhaps been the most maligned in the series. But upon my reread of AFFC, I discovered that Brienne's POV filled the void created by Arya's departure to Braavos. Arya's POV showed the conditions of the commoners of Westeros during the Game of Thrones. And even Arya's revelation of the lives of the poor failed to depict the longing for fame and fortune and then the resulting futility that comes through Septon Meribald's speech in Brienne's fifth chapter of AFFC. It may be the longest speech in the series... it may be the most honest.
I think someone noted this above... but there is a difference between the POV and the character providing the POV. Honestly, Brienne is a stupid wench. She's also honorable and yet pitiable. But her POV gives us insights that none of the others can.
Personally, I dislike Jon. I always have. But I love his POV. The NW and The Wall make for an outstanding story. Et tu, Bowen? And... I dislike Catelyn, Sam, Sansa, Theon, Cersei, and Arianne... yet I like their POVs.
I don't like Bran nor do I like his POV. But where else can I know that Bloodraven is alive, that seers look through the Face Trees, or that there was a mystery knight at Harrenhal? Nowhere else. I must read Bran to learn these secrets. And after that... everything with Jaime and Tyrion is pure joy!