I think many fans are fitted to appease the LABC inspector and once completion certificate is issued are switched off at the isolator never to be used again. Dad's house had a collection of fans fitted, bought from sheds, and one did cause me a problem as trapped in the ceiling and failed before building inspector had viewed it.
However they were seldom used, if ever, and when I came to this house, I started to wonder why this house and dad's house did not have a mould problem, but my old house in Mold did. And I realised two things, one where the replacement air comes from, and second the thermals caused within the bathroom, and main problem was having a shower in the bath, as large gap below and above the shower panels/doors encouraged air flow so whole bath room became damp, but in other house the shower door closed at bottom so no thermals causing the water vapour to fill whole bathroom.
My first house had hot air central heating, ducted to each room, and vents in every door for the air to return, we all know there should be a vent to allow air back into the bathroom, but seldom are they fitted.
Dads house got the replacement air from a cold hall, so reasonably dry, the house with problem got replacement air from a very hot landing, heat raises and it was an open plan house, so landing always hot, so replacement air cooled as it entered bathroom so humidity would rise.