What heads to unbalanced wealth is government. When the wealthy capture government to the point where they can use it to advantage themselves and DISadvantage any potential competitor, THEN you get social imbalance.
In the past you had hereditary nobility. In the present, you have "old rich" families who are heavily connected into the political class.
Rich people stay rich. Then set up protectionist policies to prevent competition. They collude with government, and such. People can throw hissy fits, but this is the reality. Piketty simply put it to paper. And at the same time, the middle class is dissolving from various trade agreements, illegal immigration, and overall global wage arbitrage.