Powell's been clear that the purpose of the rate hikes is to destroy demand until it matches what the economy can currently supply – this is practically a direct quote from his last press conference.

Supply and demand are always interchangeable when it comes to prices. We might compare supply (real GDP) to trend, and find it's been low, and conclude there's a supply and not a demand problem.[1] But the Fed is a bank and can't do much about supply.

Another question is whether inflation is actually high. There was a sharp change in the CPI last June.[2] Measuring from February 2022 still gives 6.0% but measuring from June gives 3.5%/year. There's also the question of inflation stability (2nd derivative of prices), and things have been pretty smooth since June.

So should the Fed crash the economy to try to bring stable 3.5% inflation down to 2%? Probably not. But the bigger question is: What can we do to increase supply?

[1] 1.7%/year 2022Q4/2019Q4 versus 2.6%/year 2019Q4/2016Q4 or 4.7%/year 1999Q4/1996Q4 etc.

[2] https://fred.stlouisfed.org/series/CPIAUCSL