Fine. Let's do a quick calculation.
You said creating a shaft would be as cheap as pumped storage. So I tried to find the costs involved and hit upon a price list for drilling wells.
https://haynesandsonsllc.com/wp-content/uploads/2017/02/Pric...
According to that the price for a 420 foot deep hole with a 10 inch diameter is around $30,000
Assuming we put a lead weight inside that has half the volume of the entire shaft (3.25 cubic meters) and a mass of 37 tons we end up with a stored energy of 6.5 kWh. Since the lead costs $70,000 we are looking at a price of $15,400 per kWh.
Pumped hydro is around $100 to $200.
If you use something cheap like concrete or compressed earth you can store 5 times less energy so you'd end up with even worse numbers.
And I think it goes without saying that a skyscraper is a lot more expensive than a hole in the ground.