Is this not what we have with the fan on a high bypass gas turbine engine?
The fan blades are set at a fixed angle. The engine fan RPM is varied from about 20% to 100% throughout the aircraft speed range.
Both Fan and Prop based engines will deliver power between 20% to 100% throughout the speed range. The key is how efficient is the engine producing power at certain stages of flight.
The turbo-fan engine is only efficient at high engine speeds, which is optimised for cruise flight at altitude. They burn a lot more fuel for take-off, climb and low altitude operations. You have to take this engine high to take advantage of its efficiency at altitude and speed.
A turbo-prop engine delivers more mass flow at lower speed, this allows more power to be transfered from the shaft to the airflow at greater efficiency. That is of course limited by the aerodynamics of the prop, which limits the effective speed of the aircraft.
This is why turboprops are generally more efficient for flights under about 2 hours and turbojets take over when going further.
With relevance to this conversation you would have to ask if an electric motor replacing the gas generator would be of benefit to either prop or fan.