No, because the economy has already adapted to these low interest rates. All the money that was put into high-risk instruments at relatively low yields will be desperate to move into these "low risk" bonds, which causes a huge selloff, which will be especially disastrous to those who bought in on margin.
Furthermore, those entities that have gotten used to financing old debt with ever cheaper new debt will have trouble finding new affordable debt.
> It strikes me that the problem is that the tools to fight deflation are inadequate.
What deflation? You mean the "deflation" of CPI staying below 2%? What about asset price inflation?
> How much growth and prosperity has been sacrificed to avoid the threat of inflation that never arose?
What real economic growth has been achieved by this unprecedented money-creation spree? Rising prices do not equal prosperity.
What about Japan, or the Eurozone? They have even lower interest rates and they're once again stagnating. You really believe if money was even cheaper, even more growth could be achieved?
We do have massive asset price inflation. We also have significant service-sector and rent price inflation. The CPI is only stable because productivity improvements have kept prices at bay for many consumer goods:
https://perspectives.pictet.com/wp-content/uploads/2015/04/U...
However, many of these consumer goods aren't made in the US. The dollar has been strong because, globally speaking, interest rates on it are high. If the US went back to QE and zero-interest, you could easily see a 25% drop in the value of the dollar, which immediately shows up as inflation for imported goods.