There will always be people who are able to accumulate an outsized supply of the money supply compared to others. However, in a hard-money system, it won't serve to keep poor getting poorer.

This is because the rich won't just be hoarding their Bitcoin. They will want to spend it on things and they will generally be willing to spend more on things they need than other's would, too, keeping ample supply in circulation.

Second, the reason the poor keep getting poorer under fiat is because the rich are insulated from the effects of inflation. They are typically positioned close to the money spigot, so they get to use new dollars before they can no longer buy as many goods, while the poor only get those dollars after prices of goods have adjusted upward to account for the additional supply. So the rich get the benefit of spending the new money when it still has the same purchasing power as the existing supply, and then get the added benefit of the assets they own appreciating in dollar-denominated value.

Bitcoin will flip that on its head. The other assets owned by the wealthy will no longer appreciate in value, because the money supply won't be expanding any longer. And though the poor will still have less money than the rich, that money will buy them more goods over time, instead of less. If the rich decide to hoard more of the money supply, it will only increase the value of the money that is in circulation, because there are less units of the currency available to the market chasing the same amount of goods.