I understand that some mountainous region is studying the possibility of replicating this with a funicular that would operate as the water in the dam. The losses involved in moving the funicular imply low roundtrip efficiency (the ratio of the energy recovered to the energy entered into the "battery"). And, of course, the funicular can't be used for passengers, unless there's some special discount for unpredictable schedules.
At least two people have told me about a start-up (I forgot its name) that wants to solve the battery problem by using the same approach, only with dedicated masses on vertical tracks.
The tragedy of engineering is the murder of beautiful illusions by ugly numbers.
Let's say this company can use $100\%$ roundtrip-efficient motor/generators, that is, all the electrical energy that is converted into potential energy of the moved mass can be recovered as electrical energy with zero losses in the whole process. (Yes, this is a ridiculously generous assumption, but it won't matter.)
Say this company has a 1000 metric ton mass that can be raised up to 10 meters. It can therefore accumulate $98$ megajoule (MJ) or $27.44$ kWh. Sounds ok-ish for a battery, except:
1. If that mass is made of lead (density = $11.34$ kg/l), a cheap-ish dense material, its volume is 88.2 cubic meters. That's large for a battery: it's a cube almost 4.5 meters on the side. Remember that this assumes $100\%$ roundtrip efficiency motor/generators.
2. Gasoline has an energy density of $46$ MJ/l and jet fuel has an energy density of $42$ MJ/l; using a readily available commercial-grade combined-cycle generator with a $37.5\%$ total efficiency, 98 MJ can be generated with $98/(42 \times 0.375) = 6.22$ liters of jet fuel, or less than two gallons.
Okay, the combined cycle generator takes some space, but so do the motor/generators and the support frame for the 1000 ton mass. And the space for the vertical track, of course.
Numbers. Killing illusions. No wonder so many people avoid them.
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To make up for the bursted bubble of delusion, here's the feel-good video of this week: