I have used stored energy in the form of weight but never compressed air... I had a 55 gallon drum filled with
concrete that I could raise up with a chain hoist and then let it loose, on it's way down it powered a shaft for use with various tools in the shop. A very simple but very effective stored energy system.
I have taken quite an interest in stone as a building material here in the last few years and keep thinking of how much energy one could get from mining stone at an elevation and then dropping it like the 55 gallon drum from the elevation and using the energy to power things on the trip down.
I would imagine that air can be used in much the same way, just keep in mind the 20% loss of energy each time you transform from one form of energy to another such as air pressure to mechanical, mechanical to electrical, electrical to electric motor or electrical to battery etc... It doesn't take too many times before you have little left of the initial energy you tried to store left for use.
Like Einstein stated... "simplicity is genius", the simpler the system the better the efficiency and the more viable it is likely to be for you.