vanity height
n. Unusable space at the top of a tall building created by a spire or similar extension added only to give the building extra height.

Example Citations:
Dubai’s Burj Khalifa — currently the world‘s tallest building at 2,717 feet — is topped by 800 feet of unusable ornamentation. That means almost 30 percent of the world’s tallest building is “vanity height.”
—“Editorial: ‘America’s tallest building’ goes to New York,” Chicago Tribune, November 13, 2013

Some of the world’s tallest skyscrapers have been criticised for being built with added “vanity height”, which serves no practical purpose other than to push them into the architectural category of “supertall”.
—Oscar Quine, “The height of vanity: Why taller isn’t better and the 10 vainest buildings in the world,” The Independent, September 9, 2013

Earliest Citation:
Tall buildings can be economical when it comes to saving space, high land prices and creating density, but at some point, the height of a building doesn’t have a rational meaning any more, but an emotional one. One could argue that the difference between a tall building and a skyscraper is vanity height.
—“CTBUH Mumbai Conference, 2010,” Council on Tall Buildings and Urban Habitat, February 28, 2010

Notes:

Council on Tall Buildings and Urban Habitat

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