Class distinction and hierarchy are precisely the sort of social mechanisms that convince people that there exists alternatives to certain modes of living (class aspiration).
What they are going to create a new class? Move up to the next one? Class mobility is a fallacy that was invented to support the hierarchy. Its not an alternative system in any sense.
This is patently false. Social mobility is entirely possible, although it has gotten harder since the 1980's, but that wasn't your claim.
> that was invented to support the hierarchy
The hierarchy doesn't need "support". Class and social hierarchy has been observed in every culture since time immemorial. The radical and unfounded claim is the notion that we can "remove" it in any meaningful sense.
> Its not an alternative system in any sense.
Moving into a new social class impacts your life in every conceivable way, from the way you speak, dress, behave, to the job you perform. On an individual level, it absolutely would resemble "systemic" changes to both one's material and immaterial life.