Grid-scale batteries are basically nonexistent in the US, but also aren't particularly common elsewhere. In 2016 there was only 160mW [0] of battery storage available to the grid. Battery prices have come down since then, but not enough for energy storage to make sense for utilities in a lot of cases. If capacity has doubled in the past seven years, the person you're responding to would still be asking for like 3% of available battery capacity nationwide.

As far as other storage methods, they're really cool but water and trains require a lot of space, and flywheels typically aren't well suited for storing energy for long amounts of time. That being said, pumped water is still about 10x more common than batteries right now and flywheels are useful if you want to normalize a peaky supply of electricity.

I'd like to believe we'll see more innovative stuff like you're suggesting, but I think for the time being the regulatory environment is too complicated and the capex is probably too high for anyone outside of the MAMA companies to try something like that right now.

[0] - https://www.energy.gov/policy/articles/deployment-grid-scale...

That is a "chicken farm". Nobody is going to deploy tens of millions in GPUs to something like that, let alone run their tens of millions worth of training data on that.