society
If you think a classless society is possible, do you think it is desirable?
They have not created a classless society, or even a high standard of living for everyone.
The classless society is a myth, a fact that is obvious in any ordinary secondary school.

SMART Vocabulary: related words and phrases

Class & class-consciousness in general
anti-bourgeois
anti-snob
arriviste
bougie
gentrify
go/come down in the worldidiom
go/come up in the worldidiom
heap
petty bourgeois
pleb
plebby
plebeian
the bottom of the heapidiom
the gentry
the petite bourgeoisie
the upper crust
underclass
ungenteel
ungentrified
upper class