It's cheaper to make electric motor spin fast with low torque than slow with high torque, a ceiling fan of the same cfm needs a bigger motor than a standing fan.

I would counter that a small fan spinning at high rpm makes more (annoying) noise than a large fan spinning at a lower rpm.

So it's like a lever, you aren't just magically getting more volume at the same speed without more power, it just slows down when interacting with the outside air, ie conservation of momentum

Well in fluid dynamics you don't really make the distinction between liquid and gas. You can model air as basically just a very low viscosity fluid and it works. No one really knows why it works because it shouldn't, air doesn't stick to itself, but if you pretend that it does the simulations still work, even though they're wrong.

If you look in most physics textbooks even at quite a high level they will tell you that aircraft fly because air sticks to itself, but again, it doesn't. No one is quite sure why aircraft work, no one's all that certain where the lift comes from. But physics textbooks hate to admit that so they just pretend that air sticks to itself.