Personally I think we should put big weights on pulleys in every high rise, like a grandfather clock.

How big? Seems like you would need quite a bit of weight to store any useful amount. Using this calculator: https://www.calculatorsoup.com/calculators/physics/gravitational-potential.php and assuming my values are right, if you had something the size of a bus (16,000 kg) pulled up through something as tall as the Empire State Building (380 m roof height), you'd get about 16.56 kWh, which isn't all that much. I think a typical EV battery size is about 40 kWh in comparison. With hydro storage on the other hand, you can store a shit ton of water in a reservoir without any major constraints besides the overall size, which is massive.