There are other levers that can be pulled. Taxes are one example that could be much more targeted at the specific sources of the "greed/fomo running rampant". We instead chose to take it out on everyone.
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.