Narrtive is, that yes, in combination with social distancing it should have - but people were living it up too much (gastronomy) at the same time.
Reality is probably, that masks are a mitigation strategy, but couldnt do enough to prevent multiple outbreak vectors, with which we are not so sure on where they originated. (Probably those damn foreigners that couldnt keep their infection rate low, with Europe keeping their internal borders down - or something..
) In combination with winter. (More people staying indoors again.)
Old people (good PPE regime) arent contracting it as fast as during the first outbreak f.e. This seems to indicate, that behavior (f.e. mask wearing) can mitigate infection rate.
(You dont have the 'entire old folks homes wiped out' issue italy had anymore.)