Horsepower remains a function of torque times RPM. Low RPM means low power. A fixed-pitch prop on an electric motor won't let that motor reach its rated RPM. If the pitch is low enough that it does reach RPM in the takeoff roll, it will overspeed as the airspeed increases.
The prop rpm would increase to say 2500 rpm to absorb the 100% rated power. That's the reason for the gearbox.Now, if you add a gear box so that the engine can turn 2700 rpm while the prop is turning 2300, the prop is *still* only absorbing 70-75% of total power, because you will have to reduce manifold pressure (MAP) to keep the engine from overspeeding. The torque load on the engine is reduced, which means its power output is reduced even though it's turning 2700 rpm.
The Boeing A160 helicopter has a two speed transmission for efficient loitering. Boeing A160 HummingbirdAre there any such airplanes using variable-speed prop drives?