The sort of people who set off class wars as a hobby have very particular classless societies in mind. The average left-wing revolutionary is not poor. He is a homicidal dilettante from the upper classes with a burning conviction of his own importance that he is unwilling to realize through disciplined labor. His revolution climaxes with a classless society in which he is at the very top.
Not near the top, not adjacent to the top, as he usually was before, but at the very top.