They did rapidly expand the monetary supply and it did cause inflation. Assets are sky high (stocks and real estate). Properties are priced 10-20x cash flow. Stocks are similarly trading at absurd earnings ratios.
When the Fed monetizes assets (QE) it adds to bank reserves (monetary base) AND adds to demand deposits at commercial banks (money supply) that held those assets. Where does the Fed get money to purchase the assets? They create it. Obviously no “printing” is happening it’s on a computer.
When the Fed buys the assets they add credit, giving the banks more than they need in reserves. Banks then seek to make a profit by lending that extra money, thus “stimulating” the economy.
The whole point of QE is increasing liquidity by increasing the supply of money.
Does anyone remember https://en.wikipedia.org/wiki/Japanese_asset_price_bubble ?
Massively expanding credit to the point where money is free .... reduces the value of money. But denial is a helluva drug.