Monitoring or FOQA does in no way forbid hand flying. If your company tells you it does it is the companies very much misguided approach to FOQA. If however it is the fear of being scrutinized because one is not able to hand fly one should ask himself if a seat on the flight deck is really the right place to work.
I know of several world wide operating companies that do use FOQA in some form for the last 20 years and still actively encourage manual operation of the aircraft. All modes of operation have to be known and trained by a proficient pilot, one of those is of course completely manual flight without flight director.