A distributed approach to pumped hydro might make sense. Massive reservoirs are useful, but smaller systems could also offset fossil fuel use. There are already millions of water tanks across the world that store water for households and towns. Convert them to solar and add more for other small energy uses; build enough of them and the amount of power in aggregate will be significant. While these small storage tanks could only supply small amounts of electricity, they could be enough to power many applications, and perhaps using hydraulic actuators would increase the efficiency. For example, automatic doors could all be powered by stored water pumped by solar. Add a second storage tank below so the water is re-used instead of continually consuming fresh water. Windmills could do the pumping also. There are probably millions of applications for small energy storage systems like this. Divide and conquer is another approach to scaling, and small systems are not at all tied to having suitable sites for large reservoirs.

> A distributed approach to pumped hydro might make sense. [...] There are already millions of water tanks across the world that store water for households and towns.

It really doesn't. Let's ignore that most of those tanks are in active use and can't just be filled and emptied at will so you'd need a lot of additional hardware to do anything.

The fundamental issue of gravity energy storage is that it needs a lot of height or a lot of mass (ideally both): 1kg lifted 1 meter is a bit under 10j, which is nothing (it's 2-3 seconds of a led bulb). If you have a 5000L water tank on the ground an an other on the roof of a two-story house, let's say 7 meters between the two, that's a bit under 350000J, or 97Wh, which is a laptop's battery. And that's before accounting for inefficiencies in the pumps and generators, and friction losses in the ducts.

A good PHS site has an upper reservoir capacity of millions (usually tens thereof) of cubic meters, and at least 100m hydraulic head (some are close to 1000).

You'd need absolutely humongous water towers (we're talking taller than the tallest and larger than the largest) to get decent storage in distributed completely artificial contexts: the tala tank (https://en.wikipedia.org/wiki/Tala_tank) has 1.5MWh capacity. That's a dozen electric SUVs (à la Rivian), about 20 sedans if their batteries are not too large.

Moving, lifting, and storing water are things we're pretty good at, humanity has been doing that for literally thousands of years, if it was an easy way to store energy we'd have been doing it, a lot, for a longtime.