This may have already been said but I don't have the time to read all the posts so excuse if this is a duplicate answer. Binding cut on the straight of the grain has one or two threads
running down the outside fold. Thus, those couple of threads wear out. Look at antique or vintage quilts (most of which did not use bias binding) and you can see the binding still intact on the front and the back but usually very worn and shredded on the very edge. Bias binding distributes the threads on the edge of the binding, the threads are at an oblique angle to the cut edge, thus they don't wear out as evenly. Picture a piece of striped fabric cut so that it's on the grain with the stripes parallel to the cut edges, fold it in half. See how one stripe is running down the fold? That one thread (or stripe) is getting all the wear. Now, picture that striped fabric cut on the bias. See how the stripes are slanted from one cut edge to the other? Fold the edges together. See how no one stripe is getting all the wear? That's the wear issue. If the quilt is a wallhanging or something that is not going to get a lot of wear and washing, a straight of the grain binding will be fine.
The other issue is that bias binding is easier to use on curved edges, like scallops, because it has more give.
The other time I like to use bias binding is if I am using a striped fabric and I want the candy cane stripe look.