With rising income inequality the difference between the average Joe and the 1% Joe is growing larger and larger. This seems increasingly unfair to more and more people. Eventually all those disillusioned poor people will act on this by bringing to power some radicals who will bulldoze the current system much like the Bolsheviks bulldozed the Russian empire.

If you need evidence that income inequality is itself a bad thing, ask anyone who happens to be on the poverty side of the inequality. There's much, much more of such people than rich people. All these poor people hold a lot of latent power.