As has been pointed out to you many times before, there is no need to use batteries to store utility-scale energy, so battery production capacity is immaterial. Mentioning battery production of the moment
again is disingenuous, not to say dishonest. Production capacity, anyway, increases with demand.
The key principle of bulk energy storage is E = Fx, applied liberally worldwide for centuries. It is taught to every freshman engineering student. Nothing blocks further application of the principle, at any scale.
And as has been pointed out numerous times, no existing alpine lake is needed for hydro storage. And, the site does not need substantial "transportation infrastructure". Dozens of hydro dams, still in use, were built in California's Sierra Nevada mountains in the 1920s via roads a car cannot use.