I believe that young people gravitate to Rand because she spoke for the independence of the individual, and young people don't want to think of themselves as “lazy unmotivated drones” as you so aptly stated. It is a conundrum that a young person can be attracted to Rand as well as leftist ideology at the same time. I believe it is because the average college student does not have a well-formed ideology, where they have accepted a certain world-view and rejected those things that are inconsistent with it.
When I was a college student at Indiana University during the late 1970s, a very liberal time at a very liberal campus, “Where is John Gault” graffiti was quite common.