Should the ECB really be concerned that inflation is only 1%?

It is now clear that despite the fall in unemployment, core inflation in the euro zone remains close to 1%, well below the 2% target. Is this a problem? Low inflation is a problem only if there are nominal rigidities: If low inflation leads to abnormally high real interest rates because nominal interest rates cannot be negative, deflation then becomes a problem. But this is not at all the case at present in the euro zone; If low inflation leads to abnormally high real wages relative to productivity and thus erodes corporate profitability because nominal wages are sticky, then there is a problem, even though household demand is stimulated in the short term. This configuration can be seen clearly at present in the euro zone. It is because the low inflation is skew ing income distribution to the detriment of companies, due to nominal wage stickiness , that it could be a problem today in the euro zone.