People don't want a classless society because it removes the ability to attain the one thing that all people want: distinguishment. People usually want money not for its utility, but as an arbitrary measure of merit and a way to distinguish oneself. This is why the American Dream is so pervasive: the concept of economic mobility appeals to people. If anything, we've seen a regression from equality and an exacerbation of class segregation throughout the century.
People (at least in this country) don't want to be happy and healthy. They want to be richer than everyone else because that is what success is.