Since it’s pretty clear that all of the Fed’s tightening so far has (if you believe history) not yet had any effect on inflation, this entire chain of reasoning is nonsense. Effectively, inflation has mostly cured itself with no Fed action at all.
The relevant question is whether, once the tightening has some effect on the economy, starting this summer or maybe next winter and ending within a year or so after(?), will it reach the desired endpoint? Pretending that a system with long latency should be adjusted based on current data is absurd. Skating to where the puck is now is not how you win.
And since that’s rather long and tedious, here’s some analysis:
-IGU-