Except that the Fed is not giving "government-issued financial instruments" with QE. They are placing reserve credits in the banks' reserve accounts. Bank reserves cannot be used in the wider economy, but only with-in the Federal Reserve inter-bank settlement system.
Cullen Roche has a good series of articles on quantitative easying:
* https://www.pragcap.com/understanding-quantitative-easing/
> The result has been an unprecedented increase in private cash balances -- what many call "liquidity sloshing around."
In essence, QE is/was an asset swap: bonds for reserves. There was zero net change in the balance sheet: $100M of bonds was exchanged for $100M of reserves.
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2397992