Bonny cites one of my top all-time favorite children's books in her discussion, which is Sylvester and the Magic Pebble by William Steig. Could a story in which the child character disappears early on, leaving his parents grieving for much of the book, succeed today?
One of the keys to many favorite stories is that the child is alone. Children love to explore ideas about what they could do if the limits of home and parents weren't there -- what kid could read From the Mixed-Up Files of Mrs. Basil E. Frankweiler and not imagine living in the closest museum? But the reality that today's children are almost never outside the watchful eyes of some adult closes down a lot of story possibilities.
Maybe that's why fantasy books have so much appeal right now. In those other worlds, children can be free. Which is easier for adults to take, with the children having magic powers and cloaks of invisibility and all.