The only issue I could think of with a binding formed from the backing would relate to wear. A quilt gets handled a lot by its edges, and over time, the outside edge of the backing fabric could possibly wear faster than the rest of it, making the repair more difficult.
With a standard French fold type binding which is applied separately, if it wears out, you could either splice a new section into the original or if it was really worn out, you could completely replace it.
That said, the only time I've ever heard of anyone replacing a binding was on a 10-year-old baby quilt that the child was super attached to or on a very old quilt found in a trunk or attic, etc.