The doctrine was separate but equal according to the Constitution. Segregation was not unconstitutional. Brown v. Board of Education consolidated several cases about separation, and stated that if schools were separate they were, ipso facto, not equal.
Instead of law, sociology ruled. This influenced Roe v. Wade. By the early 70s, it was thought that you must force busing of white and black races, even for several hours daily. Affirmative action always meant huge advantages given to those under the quota program. A 1983 survey by the Department of Education could not turn up a single study that found integrated schooling to have had any appreciable effect on black educational achievement.
Meanwhile, net black migration has been overwhelmingly away from the North and toward the South, the only region in the country where a majority of blacks polled say they believe they are treated equally.
Lecture 12 of 14 from Tom Woods' The Politically Incorrect Guide to American History lecture series.