How can speed and power be made independent in an airplane?
The problem is your assumption of

speed = rpm * coef

This is only true as long as there is a rigid connection between the RPM and the medium against which the speed is measured.
Let us consider a car for a moment. In a fixed gear, there is a fixed relationship between the engine RPM and the RPM at which the tires rotate. As long as the tires are not skidding, this will directly translate to a motion w.r.t. the road (against which speed is typically measured for a car). This results in the linear equation you show.
This is however not true for an airplane, where the propeller RPM does not directly translate to a speed w.r.t. the air because air is not a solid (otherwise it would be true and you can think of the propeller as a a screw that drives into the solid). Air can flow through the propeller without moving the plane. Consider e.g. a plane that is tied down on the ground and therefore cannot move w.r.t. the ground. You can still start the engine and run the propeller, which creates an airflow behind the propeller, but does not cause any movement. The same could not work with a car, as long as the tires are not allowed to skid.
In flight, the accelerated airflow behind the propeller creates thrust, which is a force that can accelerate the aircraft forwards. The actual motion will also depend on the aerodynamic forces (lift and drag) as well as gravity of course. A higher propeller RPM (at the same blade angle) will give you more thrust, but there is no rigid connection to speed.