A backing can serve to prevent a splinter from lifting on a back. If you have questionable grain or really thin rings on osage, it is a good precaution to put a rawhide or other similar backing on there to prevent splinters.
A backing can take over some of the tension work. On some designs, a sinew backing will really make a performance difference. For composite bows, like bamboo backed osage, you are gluing an extremely strong tension backing material onto an extremely strong compression belly.
A backing can protect a soft wood from damage. On yew, we often leave the sapwood for the back. It is soft and subject to damage so a rawhide bcak will protect it.
If you have a good grain on your oak bow, you will not need a backing. Many, many bows do just fine without one.