I recalled a company doing exactly that design (but 60m high), EnergyVault - I think they also had mineshaft-based projects too. The cranes stack the weights, so there's a lot more than one weight.

Checking their site, I see they currently have a 100MWh storage under construction in china, with a different, boxy-building design. No idea on costs. https://www.energyvault.com/project-cn-rudong