What if we used load bearing batteries as part of the tower structure?
Going to be a lot of flexing though.
Nice thing is that some of the “inefficient” heat may be usable on-site: and you may get compressed air as an output that could be usable directly.
Then you've got no height. Plus buildings are not dense so it's a pain in the ass, and when (not if) the jacks fail you're out a building.
Gravity is weak.