I introduced the helicopter as an extreme example in the consideration of energy used to produce given thrust. The same power producing slower airflow has to move more air and will provide higher thrust.
It's an extreme example because it's irrelevant. You're attempting to say that moving airflow more slowly produces higher thrust, which is contrary to basic physics. Now, if you were attempt to say that a substantially larger propeller disc with more area moves more airmass, then that would be correct, but it has nothing to do with the propeller speed.
We manage it in a turboprop engine at substantially slower speeds, but the RPM isn't relevant...the size of the prop and the design of the blades, as well as the angle of attack coupled with a greater torque capacity mean that more air can be moved. Light single engine piston propeller driven airpalnes have limited RPM ranges, limited propeller options, and are really no comparison to a helicopter...so introducing the helicopter is a ridiculous example.
Large props produce low speeds of flow, and note that speed of airflow comes into all the calculations, so large props behave differently. It is standard physics, the same reason a high-bypass turbofan is more efficient than a turbojet.
A turbofan is more efficient at lower altitudes, where the fan does more of the work. However, it's also a ridiculous comparison, particularly in light of the fact that most piston powered light general aviation single engine airplanes aren't turbofan powered, or turbojet powered, and the differences between the two are substantial notwithstanding the light airplane. In particular attempting to compare a propeller with a ducted fan, and a two or three blade direct driven propeller against a multi-blade ducted fan free-spool powerplant...just doesn't wash.
I was talking specifically about propellors, and in physical terms a rotor is a very large propellor, so it was relevant. It should be obvious that an R44 produces far more thrust from its 205 hp than an Arrow does from 200 hp, or the later would be able to hover on its prop.
If you were to attempt a reasonable comparison in your wild example it would be to compare the component of lift from the rotor used in forward flight, to the motive force in forward flight imparted the propeller of the Arrow...and you'd find that the propeller of the arrow is producing a substantially higher force with respect to propelling the aircraft foward through the air...and in fact even then the comparison wouldn't be adequate because of the translational lift differences of the helicopter in forward flight.
You're simply confusing the topic with ridiculous comparisons...such as the introduction of a helicopter into a discussion of glides in a fixed wing airplane.
Helicopters are also relevant if you start to make wild statements like "power doesn't achieve lift". It is a more direct example of power doing just that.
Power does not achieve lift. In the case of a helicopter, you're confused between the relative motion of the rotor...which will turn with or without power (visit autorotation), and which operates under very different principles. It's not a big propeller; it's a big wing, and it's purpose, aerodynamics, and principles are not the same as a propeller, nor is it's use. A helicopter rotor isn't a propeller; it's a wing that rotates...hence the term rotary wing.
A better comparison might be an autogyro with a propeller being driven by an engine, and a rotor producing lift in a state of autorotation. The difference between a state of auto-rotation and a driven rotor state is two-fold. The obvious difference is the motive force to turn the rotor, but the clear difference is the direction of airflow through the rotor plane.
Of course, you seem to have trouble understanding how the introduction of a light single engine piston powered general aviation airplane relates to a conversation involving light single engine piston powered general aviation airplanes...so it's no surprise that you're confused.