The challenge is with the whole concept of race, which has mostly been discarded by anthropologists et al. Very few people are now solely descended from American slaves. Most people labeled as "black" are like Obama, with European and/or native and/or mesoamerican ancestry as well, and some have African ancestry but are descended from later immigrants from Africa or the Carribbean or C. America. Also, how would we parse all the other groups, some from Europe, that were subjected to economic inequality (as some of my Irish ancestors were) or various shadowy kinds of wage slavery or indentured servitude? So what about what you suggest, looking at familial history of living where there was segregation? Is that something that can be feasibly done without creating mountains of paper to wade through? Maybe.
From my (limited) perspective, I would think you'd get more bang for your buck in looking at every personnel manager who disproportionately tosses resumes of people with names like "Chantelle" or "LaShondra" into the wastebasket without reading further. Not that I have a good handle on how to monitor that - racism is at its most pernicious, IMO, when it is subtle and hard to quantify. And, to be Captain Obvious here, start really investing in upgrading schools in poor neighborhoods and in after-school programs that stimulate young minds and engage with and expand their interests. Have a system that looks at every "at-risk" child as important and individual and reaches out to them and their families. That would cost money, but it would repay us all for millennia with a better nation, and one with far lower rates of incarceration, violent crime, drug abuse and addiction, early death, suicide, etc.