The federal funds rate is such a blunt instrument. It's not clear to me that raising the rate is particularly effective in stopping inflation, which tends to be a complex phenomenon with multiple causes. As you say, there are "other dynamics".
> people who are technically employed, live paycheck to paycheck start to rely on food banks to cover the rapid raise in cost of living - a tax on everybody.
On the other hand, there are also people who lose their paychecks entirely due to rising interest rates. The Fed has been very public about the fact that they want to stop wage inflation in particular (which tends to lag behind inflation of other goods).
It's never been clear to me why it's a good idea to continually adjust the rate, as opposed to picking an ideal target rate and trying to keep it relatively stable permanently. It seems almost inevitable that the economy will go on a roller coaster with the fed turning the volume knob up and down. Chicken and egg problem, to mix my metaphors.