The use of higher education to change social class standing in the post-WWII period was a historical anomaly; college (and education in general) had always been part of the reproduction of social class in the U.S. and elsewhere, not a part of any change in social class. The possibility that expanded opportunities for a college education have not produced quite the changes in social class standing that social engineers may have expected is not at all surprising, and might be one more example of the fallacy of assuming that education alone is the determinant of everything about an individual's life.
Indeed. The US was not only the industrial leader of the world at the end of WWII, but was also the overwhelming industrial leader, because large portions of the world were devastated. All sorts of things could work well for us then because we didn't face the economic competition that we now face. Moreover, while educating the population has certainly played its part in pushing America ahead of the rest of the world, when you educate everyone in the country then everyone benefits, which doesn't necessarily equalize people if they start from different points, and especially doesn't equalize people if the degree to which they are positioned to benefit depends on the advantages that they already have. The last point is related to Kentaro Toyama's basic argument in Geek Heresy.
Education is an important thing, but at some point you will reach a point of diminishing economic returns on educational expansion, and that's the sign that improving the economy will improve education more than improving education will improve the economy.