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In the past, we did have a need for purpose-built skyscrapers meant to house dense racks of electronic machines, but it wasn't for data centers. No, it was for telephone equipment. See the AT&T Long Lines building in NYC, a windowless monolith of a structure in Lower Manhattan. It stands at 170 meters (550 ft).
This NYC example shows that it's entirely possible for telephone equipment to build up, and was very necessary considering the cost of real estate in that city. But if we look at the difference between a telephone exchange and a data center, we quickly realize why the latter can't practically achieve skyscraper heights.
Data centers consume enormous amounts of electric power, and this produces a near-equivalent amount of heat. The chiller units for a data center are themselves estimated to consume something around a quarter of the site's power consumption, to dissipate the heat energy of the computing equipment. For a data center that's a few stories tall, the heat density per land area is enough that a roof-top chiller can cool it. But if the data center grows taller, it has a lower ratio of rooftop to interior volume.
This is not unlike the ratio of surface area to interior volume, which is a limiting factor for how large (or small) animals can be, before they overheat themselves. So even if we could mount chiller units up the sides of a building -- which we can't, because heat from the lower unit would affect an upper unit -- we still have this problem of too much heat in a limited land area.