The level of abstraction obfuscates the issue. The problem is that some people want a racial spoils system.
People generally approve of means tested public assistance, particularly for children, while many disapprove of race based public assistance. White is not a synonym for advantaged, and black is not a synonym for disadvantaged. Help the disadvantaged. Easy peasy.
If a greater percentage of blacks are disadvantaged, a greater percent can qualify for assistance, this time without the stigma associated with race based preferences.
Of course, the cost a program based on actual advantage starts to be born by the advantaged regardless of race, and not born by disadvantaged whites. I don't think it's just a fluke that the disadvantaged bear the cost of the current programs.
Help the disadvantaged. Easy peasy.
If it's that easy, can you explain precisely how you would do it?
As-is, affirmative action targets a significant number of candidates who're not particularly disadvantaged in meaningful terms, and it is a problem. But on the other hand, racism, conscious and otherwise, is still a significant enough force throughout the country that applying strictly race-blind criteria in order to assessing how disadvantaged candidates are is liable to return bad estimates in many cases.
Doing better than the current system may not be a great feat, but creating a perfectly equitable system isn't a trivial one.
Related: Heuristics for Evaluating the Soundness of the Academic Mainstream, Admitting to Bias, The Ideological Turing Test