vertical sprawl
n. The unplanned addition of a large number of high-rise buildings in a relatively small area, leading to problems with traffic, parking, and infrastructure.
Using an aerial image of the so-called "vertical sprawl," high-rise contemporary apartments of Shanghai as an example, Dittmar explored the negative trend of standardizing and effectively de-humanizing urban dwellings — lessening culture and quality of life.
—Caitlin Schudalla, “Conference at OU examines national living solutions,” The Norman Transcript, April 04, 2013
The proposed complex would bolster the entertainment district’s cultural landscape, he said, but it also opens the door to a planning dispute on the proposed 80-storey height of the condo towers.

"Managing vertical sprawl is as big a challenge as urban sprawl," Mr. Vaughan said.
1995 (earliest)
Over the years, however, the classical harmony has been eroded by buildings like Gio Ponti's 1971 Denver Art Museum, and by a typical downtown's vertical sprawl.
—Herbert Muschamp, “Architecture View: A Wonder World in the Mile High City,” The New York Times, May 07, 1995
This phrase is based on its horizontal cousin, urban sprawl, which the OED defines, tidily, as "the uncontrolled expansion of an urban area into the surrounding countryside," and traces back to 1934. Variations on the theme are suburban sprawl (1938) and, simply, sprawl (1955).