At least from the conversations I've heard about this topic, the issue isn't acknowledging that slavery and Jim Crow has caused problems for generations of blacks. The problem comes when measures to address it are discussed, like reparations or quotas. People see it as monumentally unfair because, while being black is a handicap, it's only one of many that are too endless to enumerate. For example, there is no affirmative action for poor whites who grow up in broken homes. There is no affirmative action for simply having parents who are a standard deviation below the population in IQ. Insofar as student spots at high-tier institutions go, here poor whites see favorable action to benefit blacks when they themselves never played a part in their oppression. Black, well-spoken immigrants from Nigeria who never experience discrimination in their home countries get benefits merely by dint of their skin color, and not actual suffering.
Even if you limited it to some way to only US blacks who could prove lineage to an actual enslaved individual, suffering is difficult, if not impossible, to quantify. So... why action on this topic is politically impossible. I think color-blind welfare policies based on economic resources would be much more feasible, but... good luck raising taxes to increase the size of the welfare state.