The rich hoarding wealth does directly increase money supply because they generally reinvest, which is excluded from the CPI, which decreases interest rates leading to further money supply growth. Their wealth isnt really real when viewed through the lens of monetary policy, its inflated based on past consumption and things like hedonic adjustments or substitutions.

Money velocity increases more when the poor get the money, via things like Covid stimulus, which lead to the large inflation print. While the rich just put it into assets, driving up the stock market and real estate, which made them nominally wealthier.

I think this is why QE hurts the poor and benefits the rich, their salaries are being debased to push up asset values, until someone with a propensity to consume receives that nominal windfall; whether its a home sale or an equity sale. I dont see how the rich is at fault for any of this however, and I think if they did give their money away then nominal asset values would fall and inflation would rise.

What I'd perhaps like to see is instead of dropping interest rates taxes were tied to inflation, where they rise if deflation occurs. That I could perhaps see working, though its a working theory for me at the moment.