Why does my bathroom extractor fan not clear the steam?
Usually because the fan cannot move air, rather than because the fan is broken. An extractor is only as good as the path the air takes out of the building and the path fresh air takes in to replace it.
Start with the ducting, which is the most common culprit. Flexible duct that sags, kinks or loops adds enormous resistance, and a long run of it can cut actual airflow to a fraction of the fan's rating. Rigid duct, kept as short and straight as possible, moves far more air. Check also that the duct actually goes somewhere — fans that terminate into a loft void rather than through a vent are a frequent and damaging installation error, dumping moisture into the roof space.
Then check the external grille. Backdraught flaps stick, painted-over vents block, and insects and debris fill the mesh. A grille with a fine insect screen can halve the flow.
Next, replacement air. A fan cannot extract air unless the same volume can enter. A tightly fitting modern door with no undercut and no vent effectively seals the room, and the fan strains against a partial vacuum. A 10mm gap under the door usually resolves it.
Only then look at the fan itself. Cheap axial fans are only suitable for short duct runs; anything longer needs an inline or centrifugal fan. Dust on the impeller reduces output significantly and is worth cleaning annually.
Finally, check the run-on timer. Steam takes several minutes to clear after a shower, and a fan that stops the moment the light goes off has not had time to do its job. Fifteen minutes of run-on is a reasonable setting.