Even the rich will be worse off. Just relatively less so. It's utterly irrational, but that's what happens when a population feels disillusioned with the status quo, and capital does all it can to push that unrest in any direction but reducing wealth inequality. Turns out the next easiest outlet is to appeal to humanity's worst tendencies, resulting in the rise of fascism.
This will play out over and over in liberal democracies so long as they abide a large wealth gap. It's anyone's guess whether we'll figure that out before there are no democratic states left.