I think that there is an excellent point here that "Incentives matter".

Welfare is currently designed such that married couples or even co-habitating couples are punished and given less resources to succeed. Its unclear if that was an intentional attack on the black family unit or just an unfortunate consequence but the destruction of the poor black family is one of the main consequences of that policy. This could be easily fixed by removing the marriage penalty from all government programs and actually proving a small incentive for two people to stay toughener and raise a child.

Just like incentives matter in welfare the do so in schools as well.

There is no Incentive for good teachers to teach at poor schools, and no incentive for good students to go to said poor schools so anyone that can just gets out and goes somewhere better. Because of this, schools naturally segregate. If no effort is taken to integrate them over time schools will segregate into rich schools and poor schools which also tends to mean white/asian schools vs black/Hispanic schools due to how wealth is distributed demographicaly in the US. Its a self reinforcing loop where if a school is on an upward or downward trend it will continue on that trend until it either levels off at the top or sinks to the bottom.