Your suggestion relies on the assumption that there is some way to change standardized tests such that they do not correlate with wealth. Perhaps the problem is that academic ability is directly correlated to the kind of test prep you receive, so unless you set a test paper full of trivia questions the student that has gone through test prep will perform better every time.
I do not agree with this idea either, but only in that the adversity score will be opaque to students, so there is no recourse if it does a poor job of addressing the current issues with college admissions.
