Maximum energy stored for the weight necessitates high rpm. Disintegration on overspeed is the problem. Steel becomes shrapnel. Carbon fibre becomes fuzz. For the weight carbon fibre should be able to store more energy than steel as it will be able to spin faster before destruction. The wheel is shaped such that a planned band near the rim is formed with less thickness so that on overspeed only the rim disintegrates. Like a shear pin.
Some work was done to in the late 70's to incorporate a flywheel in a coal mine in Pennsylvania, I believe. The shuttle car was to have a 5 flywheel package where the cable reel was. The flywheel would provide thru a gear box hydraulics, lights, tram and conveyor power for 20 minutes. Idea was at the feeder when dumping coal to contact the power supply and spin the wheels back up. I never did hear how the tests went. I saw that in an old Mechanix Illustrated. Since 30 years from that I've never heard of such in the coal fields I'd say that normal mining "stop and go" methods proved the idea not feasible in that application.
I think some trolley cars on the west coast were using flywheels to go beyond the trolley wire a short distance.
Still, the fibreglass and Kevlar wheels could hold considerably more energy per pound than steel because they could be spun faster.