I add that this is wrong another dimension. In my forthcoming book at University of Chicago Press, I show that growth in the gilded age was actually egalitarian.
Below is the table showing all the data improvements for the period and the evolution of (Avg_top1 income or Avg_top10 income)/(Avg_Bottom90 income).
Its just that Zucman, Piketty and Saez never bothered looking at the data and its limitations or considered improvements.
At the peak of the Gilded Age, the 4 largest fortunes were Rockefeller, Carnegie, Astor ( Baker/Frick/Field depending on the year).
If they had spent their wealth, they could have bought 4% of all the goods and services produced in a given year in the US at that time.