ehhhh.....I don't know who told you that, but they are dead wrong. A fan clutch can be a power advantage over a solid fan by allowing the clutch to coast the fan at road speed if it's a thermostatic fan. The thermostat cools down at highway speed and unlocks the clutch allowing the clutch to spin and not drive the fan, which reduces drag on the engine drastically. This is the whole reason Mopar Performance offered their viscous fan package
Again I agree with what you just said, but again it does not add to the cooling of the system.
A fixed fan will move air regardless of the temp of the air moving past it.
One could argue that the hp needed to spin the fan = heat creation so if you are not spinning a fan your engine will run cooler. But at higher speeds the air moving past the fan will be about the same as the speed of the air the fan is pushing. That means the force needed to spin the fan is negligible.
It is purely an efficiency thing, not an improved cooling thing.