If the government really wanted to entice diversity, they would let the dollars follow the minority kids. The more you have, the more money you get. Then the schools would "recruit" more minority kids.
You're only part right - in many cases when predominantly black schools degrade, it's not as much about the amount of money that flows into the school district, as much as it is about corrupt and inept administrators of those districts. The money flows in, it just does not flow down to the building level. This happens most in urban systems. And since most of those urban systems are run by liberal black administrators, the unspoken implication is allowed to fester.