But wouldn't they expend more energy moving the water up the mountain than what it will generate? Second law of thermodynamics and all, I don't see how you can give water the same potential energy it had before it flowed through the turbines.
https://en.m.wikipedia.org/wiki/Pumped-storage_hydroelectric...
The real competitor is Li-Ion batteries which now cost about the same as pumped storage, and have similar cycle efficiency. Problem is the capacity decline after a few hundred cycles, which is unfortunate if you want to build infrastructure that is low-maintenance and survives decades.
If you are interested in the area, this blog post gives some thoughts to implications [2] though it is a bit outdated by now.
[1] https://www.researchgate.net/figure/Comparison-of-various-EE... [2] https://dothemath.ucsd.edu/2011/08/nation-sized-battery/