What can make monetary policy ineffective?

In contemporary economies, central banks choose short-term interest rates and buy risk-free as well as risky bonds. Thus, they control everything: short-term and long-term interest rates as well as risk premia. So why might monetary policy not be very effective, which seems to be the case? Of course, because when interest rates are zero and risk premia are completely squeezed , it is not possible to go any further; With regard to the effect of monetary policy on households, first because there may be an income effect: low interest rates drive up the savings rate so that the income from savings stabilises; second, because borrowing capacity may be saturated; With regard to the effect of monetary policy on companies, because there may be a gap between the marginal productivity of capital and the real interest rate, which means that the fall in interest rates does not stimulate investment. This gap may be due to an abnormally high required return on equity or the proliferation of companies with dominant positions.