Despite a zero interest rate the threat of falling prices is imminent, which hurts the economy rather badly. In a famous 2002 speech, former Fed chair Ben Bernanke proposed a conceptual solution to this very situation: as the printing press is a monopoly of the state, newly printed money should be injected into the economy, which will prevent deflation. Later on he also had the opportunity to do the stunt in practice.
I have a problem with the concept of a monetary system driven by interest rates. My problem is that it will work well only in a certain range of the parameters describing the state of the economy. Interest rates may only be an efficient means of influencing inflation where debt, foreign currency debt, wealth inequality, etc. are not excessively high, but people’s expectations for future inflation also make a difference. That’s what I call the working range of the system. Outside that range, risks and side effects will increase radically.