I think this is called comunism (as Marx intended, not as was executed in the USSR, Cuba, and any other place in practice).
The problem with this is that if you don't allow for the existence of official channels the rich can use to improve their lot then there is no point in being rich, so most people will either not bother and work as little as they can to live or find unofficial channels where they can have power to improve their lives (see the communist parties in the former USSR and China).
Of course, communism can arguably work, but how to do so is still an open problem.