There have been proposals for technology like this. Putting a motor above an abandoned mineshaft and suspending a weight. Charged by raising the weight, discharges by lowering against a load.

The issues is the capacity ends up being pretty tiny, not really at a grid level.

You’d need a TON of motors to get to something a grid could actually use to stabilize, and by then the economics don’t work out. Let alone the actual space requirements of that many motors

Additionally, a lot of the advantages of batteries come from local storage, where you don’t need to transmit the energy long distances anymore, and these “natural” batteries tend to take up a lot of space.

A better and more accessible form of “natural” energy storage are already in most homes. Heat pump water heaters in homes could do things like make the water extra hot during solar hours, when power is cheap, so they can make it until the next morning without turning back on.

Or with better building envelopes (insulation) we could run more cooling during solar, maybe even make a ton of ice. Then later in the day, when solar drops and the grid load peaks, you can still cool the building with ice.