The most common explanation for the end of class in America is the introduction of merit based testing for college entrance to Ivy league schools around the time of the Korean War.
The problem with this explanation is that it wouldn't have broken down the class system. The top class would have continued to associate with each other in prep-school and in college as they always had. The same would have been true of all upper class institutions.
Moreover the end of the upper class was visible by 1960 with the last published copy of the New York Blue Book. Such a short period, ten years of college time, makes no sense in terms of a social change of such great magnitude.
A better explanation would be that WWII produced several hundred thousand men and a few women, who's army service provided them with managerial skills that were desperately needed in the rapidly expanding post war economy.
With hundreds of thousands of skilled managers entering the work force in the late 1940's we could expect to see a social change ten to fifteen years later as these men became the new meritocratic class and displaced the old aristocracy.
America was unique among nations in re-integrating its trained military managerial men back into a rapidly expanding society after a victorious war. In addition, unlike the French, German and British societies, the upper class in America was weak, fairly permeable and much too new to have staying power in the face of the arriving postwar managerial meritocrats.
WWII training of men in managerial skills was the reason the upper class lost its role in America.