To maybe put it another way, there is no way to charge a dead battery with an induction machine.
That's not true.
> You need a rotor field to generate power.
Residual magnetic field is enough to start the process, absent that a quick DC zap will do.
> In a permanent magnet machine this field comes from the magnet, but in an induction machine this comes from the motion of the stator field (Lenz' Law).
Yes. Fortunately rotors retain a bit of magnetism after you run them to a stop, which is enough to get things going again later on.
> To maybe put it another way, there is no way to charge a dead battery with an induction machine.
Yes there is, unless the induction machine is fresh from the factory and has never run at all.
As for the rotors and stators themselves, they are good old iron/steel laminates and will hold some magnetism just fine (they're laminates to cut down on the eddy currents). If the rotors themselves would be made out of copper the motor would not function at all, it needs a ferromagnetic part there to focus the field.
Source: have done a number of induction motor to windmill conversions. Also: have you ever tried any of this or are you coming at this from a theoretical angle?
Here is some good info for you:
Fortunately not everybody will take 'it can't be done' as the final answer :) It's not what can't be done in theory that matters but what can be done in practice.
I think there are other more significant trade-offs between induction and PM motors. Induction motors/generators are significantly heavier, and have significantly lower torque (i.e. can extract less lower at low speeds when used as generator). Their main attractiveness comes from lower cost, reliability, and decent efficiency at high speeds.