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.