You must be incredibly naive if you still believe BBC journalism is impartial. It has been pretty thoroughly been neutered and brought to heel by Cameron's and successive governments, and the political hacks they appointed like Richard Sharp.
The BBC is a valuable instrument of soft power for the UK government, and thus some line items like the World Service (sadly cut to the bone) really should be paid out of the Foreign Office's budget.
Including the licence fee in the Netflix bill would mean people who are already paying the licence fee would be charged for it twice.