> That is, the energy that would be required to build it would vastly exceed the total energy it could store integrated over its lifetime.

Storage ‘buys’ energy when it’s cheap and ‘sells’ it when it’s expensive, where ‘cheap’ can even mean ‘free’ at times.

You would build it using averagely priced energy (using only cheap energy is impractical, as it would keep machines and personnel tied up waiting for prices to drop)

Also, having a large buffer can mean having to spend a lot less money on excess solar and wind farms. They wouldn’t have to meet all peaks in demand.

Those still could make it economically viable.