I always thought that the "accelerated" programs in public schools perpetuate this issue. There were some very sharp kids there for sure, but it might as well have been called the "conscientious track" since it was full of children who proved that they could sit quiet, learn from reading on their own, navigate institutions, etc. All the things rich parents make their children do anyway.
I've met too many individuals since who are intelligent but disorganized, energetic, or don't have a stable family that might have actually benefitted from some special attention and encouragement, unlike all the kids who were going to be just fine anyway.