Comment by adrian_b

AFAIK, carbon fiber flywheels that are levitated in vacuum and that exceed the energy density of the metallic flywheels have already been made and used in certain experiments, even if I am not aware of any such flywheel being available commercially.

There was also some research for using such flywheels for energy recovery in very heavy vehicles with electric motors, e.g. tanks with a turbo-electric generator, but the use in a vehicle has obvious difficulties. Even if the flywheels are paired, to avoid influencing the mobility of the vehicle, that still causes high internal stresses in the case holding the pair of flywheels when the vehicle rotates, which can lead to fatigue failures.