There are downsides to inflation of course, lower economic growth is a big one. But we are entering a higher inflation, higher interest rate environment whether we like it or not, and that will result in lower wealth inequality. Money will have less direct purchasing power, and assets like housing or company equity will decline in value due to higher borrowing costs.
There are many people who will retort that 'inflation hurts the poor'. Yes, it hurts everyone, but it disproportionately hurts the rich. It is no coincidence that wealth inequality increased dramatically during the low inflation, low interest rate period we have experienced over the last two decades.