Of the many attributes I appreciate in a good binding, the one that makes the most difference when it comes to actual use is the ability to open flat.
I don't know enough about the intricacies of bookbinding to say for certain why some books open flat and others don't. It's not a question of cost. There are cheap Bibles that open flat and expensive ones that don't. Perhaps the construction of the text block makes the difference, though again, I've handled sewn bindings that open flat and others that won't. A glued paperback with a softcover will open flat, too, assuming the text block has some weight to it. Some have suggested that the tightness of the binding plays a role, which makes sense to me: with use, I've seen Bibles that wouldn't open flat start to do so. One of the things I love about Cambridge's Pitt Minion (pictured here) is that it springs open and stays flat right out of the box.
If I were publishing Bibles, this is one of the attributes I'd strive for in every edition. Whether they are luxury or economy editions, with enough care for detail and proportion, there's no reason why a Bible shouldn't open flat.