The two greatest problems with any form of collectivism are first the people in charge of redistributing wealth have too much power. This always leads to incompetence and corruption, and 2nd there is no motivation to innovate and improve.
But it has failed over and over again to eliminate poverty or end social classes. Communism creates an elite political class that rules like kings. The workers don't own the means of production or anything else. Workers live in fear and poverty.