But they are also very low-throughput.
Essentially they make the same sound, but 100's of times lower in audible volume, just as they move 100's of times less volume of air per second. (It may not be linearly scaled, but it's definitely proportional.)
Have you ever used a ceiling fan? They move plenty of air. Like I said you can recreate that tornado scene in Wizard of Oz pretty trivially. The fan is probably 3ft diameter sometimes a whole lot more. No box fan is nearly so large.