Yes the first thing to cut out is the “unearned income”.
Higher income linked to real work / productivity is unlikely to be as big a problem unless the higher paid/skilled workers start gathering market power and controlling stuff (unearned income like a monopoly premium).
But the original thought experiment seems cart about horse to me - the work and product comes first, coins come along second to make it easier to specialise and trade.
Those family guy writers will surely stop picking out idea balls now.