That kind of fan there is no any protection, so the speed can't too fast, otherwise when the fan is working and the blades left the fan that it may kill someone.
You might look inside for a capacitor and replace it with one of equal ratings and see if that helps. I have done this when fan was running slow with good success.
The old Hunter brand fans were famous for "barely moving". If everything checks out when measured, you might have to conclude that it was designed to run very slow. Still, checking its parts is a good thing. You can't be sure until you examine it.
The AC motor in a fan runs in a state of "slip" so the speed you get is determined by the input power compared to all the drag forces.
If there is a high drag force (like a bearing that needs lube) the fan will run very slow. Other symptoms of bearing drag will be that the fan is very slow, but can speed up if left running (as bearings warm up and loosen).
Spray a heap of lube in there, but pick a lube that doesn't smell too much.