Euro zone: If it is believed that there is a shortfall in demand, why let monetary policy ensure the entire adjustment?

Let us make the assumption that the euro zone ’s problem currently is a shortfall in demand (there is actually an external surplus and low inflation, and let us assume that unemployment is still higher than structural unemployment). What is the economic policy reaction to such a situation? The fiscal policy of the euro zone as a whole is restrictive; Real wages have accelerated, due to companies' hiring difficulties, but very little; Most of the stimulation of demand is ensured by zero or negative interest rates, i.e. by monetary policy. This choice is unbalanced, and probably not very wise given the many drawbacks of very low interest rates income (income effects on savings, real estate bubble, weakening of banks, support for inefficient companies).