I would never burn a book for its content. I would however, burn a book because it is made paper, which is very flammable. If the option is me and the last copy of the greatest piece of literature written in the history of forever, everywhere, written on paper? It probably won't last long after my death anyways. Better to burn and give me heat for one more day.
Oh, I would also burn anything mass-produced, but falling apart, 'cuz, I dunno, we found a box of old romance novels in the cottage and there's a fire pit outside and we need paper to build up the flame. Or something.
And I've cut up books for artistic purposes, using parts of pages in mix media projects. But only if the book is falling apart and I have no attachment to it. Even shitty books, if new, I'd rather turn into a second hand bookstore for the pennies per book I would get. The stuff even they won't take? Meh, I could care less. But never, ever would I burn a book for its content.