1. It's a known fact that the bigger you make a propeller/impeller/fan, the less horsepower it needs to move a set amount of air...
Well, it's not well known to me, and I've worked on performance of large fans for several decades.
You seem to have overlooked the role of the fan duct and nozzle. For a given fan diameter and RPM, you might choose a small-area nozzle, meaning the exit velocity will be quite high (but still subsonic) - with two implications: Lotsa noise, and lotsa horsepower (fan shaft torque) required to pump up that much air pressure.
Or, you might choose a larger exit area, less air pressure, less exit velocity, less noise, less hp required.
It's all a matter of what best matches the aircraft's mission.