You're making a foolish assumption that many economists made and I will completely destroy it through an unrelated problem.
That is, monetarists assume a constant circulation velocity of money. i.e. hoarding of money doesn't exist.
This is extremely foolish because it would mean the existence of a debt crisis would be impossible. Every dollar the government spends will circulate and as it circulates it will get taxed. It's impossible for the government to be insolvent or go bankrupt. The truth is that the government cannot repay at any arbitrary interest rate. It takes time for the money to circulate until it is 99.99% taxed out of the economy. That delay effectively determines the interest rate the government can afford to pay. Companies and the rich are strongly incentivized to minimize their tax burden. If they find a way to never pay the money back then the interest rate would have to be 0% or even negative.
This doesn't work for the average household that is paying income tax. It cannot hide from taxation forever. In other words, the money that isn't returning to the government also isn't being used to hire people. The mythical constant circulation velocity simply isn't happening. In fact, it's dropping. You constantly have to add more money into the system just to maintain the same velocity. That constant velocity is needed to maintain full employment.
What inflation does is take money that is stuck in the untaxed section of the economy and tax it immediately.
>If people really cared about inequality, wouldn't they want deflation?
Deflation benefits the rich because they can acquire bigger piles of Bitcoin than you can. How difficult is that to understand?
>Deflation would see wage earners purchasing power increase while the wealthy people's assets would depreciate.
Wealthy people would just have money be their primary asset. Considering that money is needed to pay incomes it doesn't sound like a very good idea. Your boss pays you according to the value you produce, if the money supply contracts/price levels fall off then the products you produce are worth less meaning you have to take a pay cut or get laid off.
>This would definitely lower the Gini coefficient.
You just shifted wealth from one asset to another. How does that change anything?
>But the wealthy people who control monetary policy would never want to see their assets deflate so we will never see a deflationary monetary policy, which could help wealth inequality.
What the hell is wrong with people nowadays? 20 years of low 2% inflation has rotten their brain and made them think inflation is out there to get them. If deflation is really all that great why hasn't it reduced inequality by now?