The triple contraction in demand if central banks combat inflation

If central banks really combat inflation and raise real interest rates sharply, there will be a triple contraction in demand for goods and services: Directly, due to higher real interest rates; Through negative wealth effects due to a fall in asset prices; Through the inability to keep fiscal policies expansionary if real interest rates normalise. The cost of combating inflation in terms of lost activity and jobs would (will?) therefore be very high.