Is anyone arguing that the Fed is responsible for "total price levels"?

The fed funds rate is used as the foundation for nearly all lending that occurs in the US, and setting it is a key tool for regulating credit (the only job they have per this paper).

The paper also lays out how credit/money creation and destruction impacts the overall economy, so I can see how the Fed's actions related to regulating credit impact overall prices, but it's a second order effect at best and there doesn't seem to be any reasonable alternative?

I guess the issue is that the paper keeps talking about inflation caused by "supply-side issues", as if the cause of inflation can be clearly discerned at any point in time or that whatever inflation is caused by supply-side issues isn't tightly linked to the amount of credit available and therefore would fall under the purview of the Fed?

The Fed is responsible for controlling inflation; if taxation of excess business growth (relative to household spending power) beyond the inflation target serves that purpose, then how businesses choose to spend the excess growth (to avoid tax penalties) — either by lowering the price level and/or raising total wages paid — is entirely up to each business to determine in their specific circumstance and industry.

I don't understand your point.

I agree tax rates are disinflationary in theory and I believe in practice to an extent, so it could be another tool in the Fed's toolbox but not one I think they want to have or one that Congress is willing (or arguably able on their own, though they wouldn't have to if the Fed's role were just advisory) to give up.

But what does that have to do with the paper you posted?

Ah, we both agree on the reality of an unwilling Congress, for sure :) I misunderstood your request for a paper as topic unfamiliarity, apologies; feel free to disregard the link posted.