Of course, it didn't really turn out that way, did it? Government got more powerful. Sure, the power was expressed differently, and in a "better" way. But still, government power was (and is) used to mandate social situations in the US. Affirmative Action is just one example where, if the skin-color of the participants is not pleasing to the politicians, then the full power of the federal government can be brought to bear on the transgressors.
That may (perhaps) be better than Jim Crow. But it's not all that different, really. I just think that less government intervention would have allowed citizens and businesses to make their own decisions. Government solutions are rarely good solutions.
The US has by-and-large imposed government solutions to our problems with race relations. How well do you think has turned out?
I generally agree that, political rights aside, government is a poor way to achieve racial harmony. My point is simply that Jim Crow was a disaster precisely because it was government intervention, on the side of mandatory segregation.
About as well as any government imposed solution works, but in the case of racial discrimination the condition today is vastly imporved from that of 50 years ago.