I would think the cables would break just from their own weight, much less a huge building attached.
Plus that asteroid won’t stay in orbit with a constant pull downward......................
Not just the gravitational pull, but also the atmospheric drag from pulling a skyscraper through the air at 1,000 mph.
On the other hand, the massive electrical discharges created by the static electricity generated from pulling a skyscraper through the air at supersonic speeds will go nicely with the constant sonic booms.