The problem with doing it at the admission level is you have to adjust ALL admissions processes. Doing it at the SAT level avoids the problem where disadvantaged kids are cut off by hard score limits right at the start of the process.

It could also be used to signal to schools which kids are likely to need some remedial classes in the first year despite what they scored on the SAT. Of course one can imagine a scenario where the admissions looks at the adversity score to weed out kids who they don't think are going to be prepared regardless of how smart they are.

This whole process assumes that the universities are interested in reforming the kids that the school system failed in the first place.