It's not so much that the Fed’s “hands are tied” preventing them from monetary policy they should, as a central bank, take. Rather, Congress just isn't taking fiscal policy actions that they, as the government outside of the central bank, should take, and (in some cases, especially on the Right) blaming the Fed for for their own nonfeasance.
I mean the Fed didn't even flinch at all in 2021 as all asset valuations reached bubble territory. Real estate appreciated faster than anytime in history. This becomes a real liability down the line if normalization of policy is ever needed. Bubbles can be disastrous to the economy longer term.
They removed the moral hazard of risk taking for the past decade or so.
The policy response to 2008 has shown that next to nothing is going to happen on the fiscal side (though this did change in response to COVID, hopefully this is a positive sign), so the fed has been backed into a corner without a whole lot of room to run.
When a major swing happens, if they do nothing, then it’s “the fed let a recession happen!!!”
Instead they addressed the acute crisis, and continued the same policy for 2 years with no change.
What they should have done was 6 months or so after peak covid panic, start to normalize interest rates and QE. They also didn't consider at all the velocity of the economy and just looked at point in time employment numbers to drive their policy thinking.
It was clear the job market was already overheated at 5% unemployment, for example, due to the historical number of job openings and increasing pace of those job openings, plus record high quits rate. Plus retail sales/inflation.
In a lot of ways, the feds hands are tied by the political dysfunction in our political branches. They’re just putzing along, trying to plug the holes in a leaky ship.