The other problem is that affirmative action (as currently practiced), is a very blunt instrument to mitigate the problems you describe. If your concern is fairness to people from underfunded schools, then discrimanate in favor of students from such schools. Currently, colleges do the opposite, since they use their historicall records to favor students that come from schools which have a history of producing students that do well at said college.

The result of that is that the bennificiaries of AA tend to be the members of the target group who least need the help, and for whom the underlying justification is least relevent.