I have never thought of doing it this way. Being self taught and getting tips from quilters when I hit a snag, I was only taught how to do the binding with a seperate piece. I agree with others when they said that it will wear faster, however if you have enough to make it double then I don't see how that won't make it last just as long as the other way. I have tied a couple of quilts myself and they have come out very nice.
If quilting and sewing is our hobby, then we deserve to do it in a way that is pleasing to us.