The actual facility is one cost. Others include extending the grid to your new generators, and the benefit of the system in the article compared to those built out of mountains, etc, is that it can be easily built on the sites of abandoned power stations, which have all the infrastructure in place (or at least resurrectible).
I love these ideas though, including yours. As the article points out, it's definitely an investment area worth getting into.
Existing, but abandoned, mines also work as prospective sites. They usually have a large vertical drop, and they often have existing energy infrastructure "wiring" them into the grid.
I'd love to see some of the deepest mines in the world turned into gravity storage systems. Some of them are in areas that are amazing for solar, so you could hook the solar up to a motor to lift the weights, and then use the weight to power generators on the way back down.
Are there any motor designs that work close to equivalently as generators? If so then the system can be simple and self switching. If the energy from the solar is strong enough it lifts the weight, if it's not, it generates electricity.
I love these ideas though, including yours. As the article points out, it's definitely an investment area worth getting into.