Except it is already being done by multiple companies [0], Energy Vault in Switzerland [1], Gravitricity in Scotland [2], New Energy Lets go [3], and Gravity Power [4]. All have raised substantial funds and are building.
Sure, pumped hydro has advantages, but has serious geographic limitations - you need a fairly ideal site. The key is that these can be built almost anywhere.
[0] https://spectrum.ieee.org/gravity-energy-storage-will-show-i... [1] https://www.energyvault.com/ [2] https://www.gravitricity.com/#about [3] https://n-e-l-g.de/ [4] https://www.gravitypower.net/