For any fan to remove air there must be a way for the air to enter the room or all it does is create and negative pressure with no flow. Most 4" fans will remove steam quite well if air can get into the room to replace it. In fact most people complain they cause too much draft. If when you open the bathroom door the steam flows into the rest of the house than maybe you need another one but if it draws in clear air and the bathroom clears once the door is open then you need more space for new air to enter the bathroom. Some countries do install heat exchange systems where cold air in is divided by only a thin skin from hot going out but not in UK.
Another problem where piped is crushed or broken pipe. But most fans are about the same and either work or don't work.
People do seem to expect air to by magic arrive in rooms we have flues, Tumble driers, and fans all sucking out but nothing blowing cold dry air in.
Hi, if fan is connected to duct more than abt 2mtrs long then a normal blade fan won't do, you need a centrifugal drum type impeller fan, also many heat exchanger types, known as 'heat recovery units' are now having to be installed in uk due to Part-L of bldg regs energy efficiency rules for new build, but are quite expensive, they are all centrifugal types.
Erics comments abt replacing air are of course quite correct, we used to rely on poor fitting doors allowing air (draughts) to get in but if whole house draughtproof then not very much good, again heat recovery units bring in fresh dry air warmed by outgoing warm/damp air so cut down on condensation also, well worth a look,