Loneviking,
The arrow doesn't care what throws it, you are right, but it will be thrown alot faster by a bow made of material that when bent, straightens back up very quickly.
It will straighten back up quicklly if it has those strong but elastic properties but also if it as light as possible. Some woods have those inherent properties more so than others so when we want the most efficient bows we chose woods that will bend, not break, not set, and straighten up as fast as possible with the least amount of material for the draw weight that we want.
So if you take a perfectly good shooting bow and laminate on a strip of rubber on the back, in order to protect yourself when it explodes, or to keep it from exploding, you are adding material that is very elastic but also very heavy. So you'll slow your limbs down from straightening back up. Rubber doesn't want to straighten back up very quickly. If you glued on a strip of carbon fiber to hold your bow together then you would notice it would straighten back up quickly, but it would also be harder to pull back where as the same amount of rubber would affect the draw weight less. So the carbon fiber is helping your arrow and the rubber is hurting it.