> Here's an idea: what if -- instead of digging a deep hole into the ground -- we use the tower of a wind turbine as the vertical space in which the weight is raised/lowered?
First, there's not really any room in there, wind towers are built for the job, we don't add twice the amount of steel and an elevator shaft for funsies.
Second, even if there were some room it would be inconsequential, you need a lot of crap very high up to get significant amount of energy.
As demo, let us take the largest turbine available right now and lift the entire thing up and down its tower.
The Haliade-X has a hub height of 150m, a 600t nacelle, and 165t blades. In normal operations it's rated for 14MWe.
765t at 150m is 250kWh. You can get electric buses with larger battery packs than that. For reference, US households use about 29kWh/day.
That's the issue with gravity: it's really not that strong, so to store significant amounts of energy you need either ridiculous amounts of weight (hence dams and pumped hydro which can manage unfathomable weights), or extreme height difference (hence… still dams, pumped hydro a bit less so I think).
As a point of comparison, Bath County (the largest pumped-storage station in the world) has a hydraulic head of 270~385m and the upper reservoir stores 44 million tons of water.
Now taking in account that you can't really empty the entire thing, that it's not perfectly efficient, etc… Bath has a storage capacity of "only" 24GWh, it's not actually moving 44 million tons up and down 400m.