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Extra complexity with more moving parts. Would be far simpler to have a coil inside with a strong magnet on the piston rod, just like those "Faraday Flashlights". Add a big enough bridge rectifier and a smoothing capacitor and bumpy roads get you back a bit of juice.
The best ones of those flashlights will levitate the magnet partway in the coil. Something to do with the way their circuitry is done so the counter-EMF generated by the magnet moving through the coil is strong enough to hold up the magnet instead of letting it drop. (Sort of a useless perpetual non-motion machine. With the flashlight on end the magnet will levitate forever, but one can't get any energy or work out of it.)
It takes just a bit of force to overcome the suspension and generate power. Done right, the levitation feature would aid in suspension damping.
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