In theory there is nothing wrong with the theory, but in practice it's broken.
The SATs were never supposed to be one of only a few criteria deciding admissions, but that's exactly what happened. Test scores are black and white, no pun intended, and in a sea of subjective criteria, it's hard not to lean heavily on GPA or a test score that makes decisions easy--and defensible even to a degree.
Like it or not, the way they were and likely would be used would benefit the wealthy and racial groups who already have many advantages.
Their strongest correlation the SAT has is the ability to identify the socioeconomic status of a tester's parents. When that is the result, it's impossible to make it not be used regressively.