For almost half a century, New York City held the title for the world’s tallest building. Between 1931 and 1972, the iconic Empire State Building remained the highest — standing at 1,454 feet tall.

For 92 minutes on a clear Sunday morning in Taipei, thousands of spectators with jittery nerves stared upwards, while people across the world were glued to their screens, as famed climber Alex Honnold ...