Actually, I like the battlefields a lot. Sometimes I'm in the mood to follow the story and have fun with quests - sometimes I'm in the mood to hack/slash/and advance my characters.
It's nice being able to choose which one I want to do at the time.
As for the story - they have done a great job with the story as it is - I don't need it to carry over to the battlefields.
I share this view. There are times, especially when stuck trying to figure out how to solve a puzzle, or tired after work, that I just want to go hack and slash through some stuff gathering goodies and exp without much thinking about it. The battle fields are ideal for this purpose.
They also seem to me to have the advantage that was intended--if you are stuck, go gather some goodies and exp, and try again--rather than just reloading a battle for the umpteenth time. They not only add to your exp, the foes are easy enough to make this a good place to experiment with new skills, tactics, or spells.
Now, though I am normally a completist, there is no way in the world I am planning to do every task in every battlefield--but still I am glad to have them around.