A big thing to consider when tweaking this way is racial balance. Some races are balanced based on their ability score bonuses, and changing/removing them can upset this balance (some of which is already upset, but that's another argument).
I'd suggest you take a concept from the D&D Next playtest that I loved, but was removed: each race got a +1 bonus, and each class got a +1 bonus. With the end result that most races receive a +2 and a +1 from sub-race, I'd suggest that you reduce the +2 by 1, then have each class give +1 to the primary ability (or a choice for some classes). A few races will require some extra work, especially base human, but I feel this a better solution to fix your problem.