It is definitely a confounding variable in the context of the question at hand (posed by the GP commenter): why inequality is a bad thing, and whether it is directly responsible for the "shrinking middle class" going to the "lower class" instead of the "upper class".
Historically, the middle class has been shrinking because the upper class has been rising. Insofar as that hasn't been the case since 2000, it's not because of the mere existence of billionaires, it's because of a specific type of financial instrument (in one case), and a one-in-a-century global pandemic (in another case). The mere existence of Bill Gates et al did not cause either the credit default swap crisis or COVID-19.
Sure, but the root cause of that is pretty well known to be the proliferation of credit default swaps that led to a housing bubble that burst in 2008, and not the mere existence of billionaires writ large.
> The analyses presented here confirm the broadly accepted picture of rising income inequality and slowing income growth for middle-class Americans. But a few additional points are worth drawing out. First, while the benefits of economic growth have not accrued equally, they have not gone solely to the top 1%. The upper middle class has grown. Second, the main reason for the shrinking of the middle class (defined in absolute terms) is the increase in the number of people with higher incomes.