The sort of battery you describe is utterly non-viable. The amount of energy you can store with solid blocks is extremely small relative to the cost of the structure. Do the math. With 100 tons weight and 100 meters lift (an enormous structure) you get something like 1 (one) dollar worth of electricity, which is bupkis.

Pumped storage works, because it pumps absolutely enormous amounts of water. You can't handle comparable amounts of solid blocks similarly easily.