A regular BLDC motor is already using induction. See this video.

The 70% number you are referring to is for a flat coil through a much greater distance than would be needed here. For the new design, I imagine another set of coils inside and separated from the rotor, and the magnets on the rotor replaced by a simple ring. The induction coils would need to be offset to produce torque on the ring. Yes, it would be less efficient because you are using power to produce the magnetic field. However, no rare earth metals are required.