Can there be a mile-high skyscraper?

In 1956, Frank Lloyd Wright proposed the Illinois Sky-City, a skyscraper taller than one mile (~1,600 meters). That's more than twice the height of Dubai's Burj Khalifa, currently the tallest structure in the world. In the video above, Dutch architest Stefan Al asks 'Will there ever be a mile-high skyscraper?'
If it happens, there should be a rooftop bar named... the Mile-High Club.