I've had extra 5" piano key border in the past that I cut in 1/2 and made into binding. On purpose!!! If you have the time and you want it, do it. It has been stated that it will make it bulky. Big deal. Sew what! If the look you're going for is do-able, I say "Do it!" It will be a little of a pain in the butt if you hand sew on 1/2 of the binding. Many seams, make for hand sewing through many layers. But in the long run, no one will notice that they're only 2 1/2" pieces. Galloping horse, right?
Good luck with your decision and your quilt. No need to toss or re-use. Use that material for it's original purpose! I'd love to hear from you if you decide to use it after all!