As I said below (or possibly above) this material is only energy-dense when it's in its most compressed state. To get the energy out you have to expand it again, at which point you find that you need a vast apparatus to store your energy.
Remember, the state of the art in energy storage is a metal tank filled with liquid hydrocarbons. It's pretty damn hard to beat for price, reliability, safety [ * ] and energy density. What we really want is a more efficient way of producing those hydrocarbons out of water, CO2 and energy.
[ * ] Relative to most ways of storing large quantities of energy, that is.
Also as long as you don't care about energy leakage -- no matter how good your bearings are, they're imperfect. Flywheels store energy for minutes or hours, batteries for days or weeks, non-volatile hydrocarbons for millions of years.