> If the rich getting richer drives up inflation

Big if! (Inflation drives both price levels and wages.)

We're talking about the poor here, not the middle class. A lot of states haven't raised their minimum wage above the federal minimum wage, which hasn't been raised since 2009.

Also even if wages go up inflation still reduces the wealth owned by the middle class. Especially given that interest rates on savings hasn't kept pace with inflation for decades. So unless you own a house or a stock portfolio even the middle class gets poorer due to inflation.

We have zero evidence inequality drives inflation.

Sure that's an if, but the effects of inflation certainly exacerbates that inequality. Thus the rich get richer while the poor get poorer. It's just a question of cause and effect.

> It's just a question of cause and effect

Yes. That’s a pretty critical question.

High inflation drives inequality. (Moderate depends on the savings rate.) We have zero evidence inequality drives inflation.