It would be simple enough for a DM to construct a listing of common backgrounds for races in their setting. This would act as a somewhat broadened set of potential racial stat bonuses. A player with a concept that goes against type could then pick a background outside of this list, and easily make a character that is both mechanically sound and consistent with RP.
Or... they could pick one of the common backgrounds and play with a stat spread that is not specifically optimized for their class and role, just as they can now.