Of course there is little social mobility in a classless society like the United States. If there are no class differences then, by definition, it is not possible to move to a different class. In the United States, there do exist large differences in personal wealth and opportunity but these are based entirely on personal worthiness rather than social class. The point is well made in the following clip taken from The Ayn Rand Institute's annual presentation of, "Them that have - deserve more, and them that have little - deserve nothing."
ABOVE: A group of the most privileged, and therefore most virtuous, political elite meet to work out details of new social legislation.