I'd put taxation in the same bucket as price control because for this to be effective the taxes would need to be on the rich (in effect to drain liquidity) and that's as likely as price control.
I don't disagree with the unlikely nature of new taxes on the rich. That was basically my original point. It is wild that we decided that we would rather go into a recession than tax the rich and I don't understand why there is seemingly no public pushback against this.
There's historic precedence that increasing rates controls inflation. Yes, it's a very blunt and crude instrument. However, when you know this tool works, trying another tool is too risky to experiment with (in case it fails).
Inflation does have the risk of getting out of hand and being even harder to control. The risk analysis is that whatever pain increasing the rates would cause it pales in comparison to having hyperinflation.
As far as the lack of a pushback: My guess is a combination of apathy and the fact that it doesn't affect the average person quite as much as inflation.
