The good news is that even though bindings cut on the straight of grain do wear more quickly it still takes years for those signs of wear to show unless the binding fabric was of inferior quality, then it might show signs of wear more quickly. Either way, by the time the edge starts to show wear the quilt will be outgrown. If it has become a sentimental attachment for the giftee, the even better news is, binding is easy to replace. You can cut it off, remove it by seam ripper, or you can simply sew a new binding over the old.