Three houses, my house had a problem with steam and mould, no fan, mothers bathroom never had a problem with mould or steam but it was a wet room, fan installed but never used, new house fan does not work, but no mould build up or steam problem, so I sat back and wondered why, then it hit me, the gap under the shower panel, the house with a problem shower in the bath so the glass door has no seal at bottom, so run shower and the chimney effect means water vapour is circulated around the room, but mothers house no glass panel and new house panel seals at bottom so no circulation.
Fan on after the shower clears the room, fan on during the shower can pull the moisture into the room when without it the water would go down the drain. It will depend on room design and shower panel design, and size of shower area, always intended to fit curtain in mothers shower after she died but never got around to it, she was in a wheel chair so curtains would have got in the way, shower tray well whole of floor was heated, but rarely turned on. But after a shower always mopped the floor, use of anti slip mats and the like retains the water, as do carpets.
But main thing is to keep water where the tray and drain is, don't suck it into rest of room.