If you drop a steel weight down the same well of cross-section A and height H in the same units the energy stored is 0.08HA(D-H) MJ[2]. Again, H is in meters, and AD > A(D-H), and in order to beat compressed air 0.08H > 10, so your steel weight needs to be 10/0.08 = 125 meters long! That's taller than most of the buildings in downtown San Francisco -- and in order to get any use out of this thing, your hole should be at least twice that deep.
Of course, compressed air has its inefficiencies and complexity, but the feasibility of a metal rod even close to that long seems pretty low to me. Compressed-air caverns use as much as 7.5 MPa, but a purpose-built well could potentially go much higher. Plus you don't have to deal with the damn thing vibrating from Coriolis forces and seismicity.
Now, I know what you're saying -- you're saying, if you're so smart, why don't you do it? -- but there are simply too many huge caverns out there to even think about constructing CAES chambers. There are several GW in service today. And even with that huge resource people wonder if batteries won't simply corner the market. Storage is getting here painfully slow, it seems like, but the competition is very fierce.
1: True isothermal decompression cycles are impossible, so of course I'm approximating by using the ideal gas law.
2: (8000 kg/m^3)(10 m/s^2)/(mega = 1000000) = 0.08