There are enormous inefficiencies in the conversion processes. Storing energy in a chemical accumulator also involves changing AC to DC and retrieving it to feed back into the AC grid also involves more inefficiencies.

There used to be large storage flywheels - some were used in buses a while ago - they may have the ability to to produce AC output, but you then need to have a very precise match between the frequencies or else you get severe problems that may cause destruction of the equipment.