When I was in school (mid 70s) there was work being done on "super-flywheels," both for automotive use and for fixed energy storage. Flywheels can deliver (or accept) virtually unlimited power -- not unlimited energy, but if you need a burst of power in a very short time, your limitation is not going to be the flywheel.
One of the applications I read about then was for a university particle accelerator. The local city got upset at having the lights dim all over the city when they fired it up, so they spent hours spinning up a flywheel to release it in milliseconds.
This is handy for vehicles, since batteries can't accept or deliver power as rapidly as flywheels can and that limits both braking and acceleration. On the other hand, in an accident, being able to release power rapidly is more dangerous.
Super-flywheels, incidentally, were made of fiber based materials spinning at very high speeds, just like described here. They had the same or higher energy density as metal flywheels but failed less catastrophically. Metal flywheels tend to chunk when they fail, the fiber materials to shred.