Friedman did not discuss improving educational quality for African Americans or Latinos or poor Whites in Appalachia. He did not even claim that private schools would be more academically effective than public schools. Rather, he focused on the superiority of markets over government bureaucracies in providing the greatest amount of consumer satisfaction and probably lower costs for a given amount of satisfaction. In other words, in a market you could get choice and the same amount of education for fewer resources, but not necessarily better education for the same resources. Much of the demand for educational alternatives is also coming from that same population.
More choice is certainly a desirable goal in education.
If anything, private choice has traditionally responded by ignoring or even exacerbating class, racial, and ethnic segregation and inequality.