Hi doma,
I think that by supporting their currencies, central banks think they are stabilising one portion of the economy upon which people depend.
Sometimes support means reducing high inflation (the waning value of money). Sometimes it means diluting the value of money (when deflation makes both consumption and investment unappealing).
We are facing the latter, and QE is the banks' principal remedy at the moment.
The cost is borne by savers, that is true. Indeed, it is the point. The aim is to get people buying and investing again. A currency that harms an economy is not a desirable phenomenon, either way. Sometimes, it is the case that collective thriftiness is harmful to society. Paradoxical, I know.