Good question. OD obviously is the main skill used to defend jump shots and 3 pointers. But it also affects offensive flow, handling, and passing of big men.
It is my understanding that when the ball is passed into the post, if there is no shot opportunity, the big will pass it out to the perimeter. If the defender has alot of OD he will make that pass out to the perimeter more difficult. If the shot clock is winding down, the big may force up bad shot that he would not otherwise take. This happens alot because many bigs have very bad passing and handling.
Having OD on all your bigs is also important for defending against outside offense. Most people that run outside offense have at least some JS on their center.