Another advantage to a separate binding is that often a quilt will show more wear around the edges. If a separate binding was used it can easily be removed and replaced.

It's true that a double-layer bias binding wears better than a double-layer straight grain binding, and that both of these wear better than a backing folded over to the front.

I think one of the reasons straight-grain binding has become more common is that it's easier for new quilters to work on the straight-of-grain than the bias. Also, these days we are often not so concerned about making a quilt that will last for several generations; we are satisfied with just finishing the quilt! So there is less concern about using the very best method for binding, and more concern about just getting it done.