A fan that runs only when the light is on stops long before the room has dried. A shower generates moisture for 30 minutes. The air in the room becomes saturated with humidity. Once the shower is over, if the fan stops when the light turns off, the moisture stays in the room, condensing on surfaces and lingering in the air. Mirror fog takes an hour to clear if the fan is not running. Damp lingers on textiles and in the air. The room feels wet because it is wet.
The control strategy is what determines whether a fan is present or effective. A timer that runs the fan for 20 or 30 minutes after the light is off lets moisture actually leave the room before humidity condenses on cold surfaces. A humidity sensor that runs the fan as long as the air is damp is even better — it adapts to how much moisture was actually generated and runs only as long as needed. No control strategy, just light-switch operation, is the ordinary everyday failure mode of most bathroom ventilation systems. Most people assume a fan works when it is turned on, without realizing that the fan must run long after the shower ends for the room to actually dry.
Extraction capacity — the CFM (cubic feet per minute) the fan is rated for — matters significantly against the room's volume. A fan sized for a 200-square-foot room works very differently in a 300-square-foot room. The same unit might be installed in both, but it is undersized for the larger space and cannot extract moisture fast enough to prevent the room from staying damp. The extraction capacity must be determined by how the room is actually used and its volume, not by picking an arbitrary standard fan from a catalog.
Mirror fog clearing slowly and damp lingering after a shower point at control strategy, not at the fan unit itself. A powerful high-CFM fan on a light switch is ineffective because it stops too soon. A modest, smaller fan on a run-on timer or humidity sensor is much more effective because it runs long enough for the room to actually dry. The questions worth asking before the fan is specified are: What is the extraction capacity versus the room volume? What control strategy comes with it? How long does it run after someone uses the shower? How is it monitored to know when the room is actually dry?