Since scale and locality is such an issue here, I wonder if there are any concepts for integrating such a system in new mid-rise buildings. Similar to an elevator shaft, but with a weight of depleted uranium instead of the passenger car.

You're digging for the foundation anyway, maybe maybe the marginal cost to dig a few meters deeper is worth it. You're building with a crane anyway, maybe the marginal cost to build a steel frame tower on the roof is worth it. It's certainly not a mine shaft, but perhaps better than nothing.