No Stupid Questions

Weight. If you load a 42u rack up with 30lb servers you're at 1280lbs spread out over about 4sqft, which is over the floor loading limit for most buildings. It's much cheaper to support the weight in a wider building compared to a taller one.

That being said I've been in many data centers in the middle of a giant office towers, but they have lower weight limits generally.

Most obvious reason that comes to mind is cooling. All the HVAC in the world isnt going to be able to stop 50 floors of server rack heat from spilling onto the 51st floor, etc.

This is also a nightmare for fire suppression systems.

Electricity has a hard time flowing up and requires a special pumping system.

I used to have a rack in a colo in the middle of Portland Oregon. The 3rd floor was the colo and they also had telecom equipment on the roof, but the rest of the building was normal commercial real-estate.

They spent so much reinforcing the floor, sound proofing the floor and ceiling, building a giant door in the wall (so they could crane in equipment), and helping pay for a new local substation that when P.a.a.S. services (AWS, Azure, etc) started they quickly started to struggle to keep the bills paid.

Soundproofing wouldn't be needed if the whole building were servers, but the rest would be.

There are a few skyscraper server farms, but they are usually in major metropolitan areas like Manhattan. But, as you touched on, it is usually cheaper to build out instead of up.

Cost. It's slightly cheaper. And I do mean slightly.

Tall data centers do exist in cities where land is expensive. It's the same reason everyone builds up in cities. Where land is cheap and available it's usually easier and less expensive to build things low and wide.

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.

Probably a combination of it being cheaper (as the others said) and data centers not really having to be near right next to cities. It's easier to plop them in the middle of nowhere.

Taller is more expensive. That's all.
If you have the space to go wider, that's what everyone does.

The taller it goes the more they'll have to value human life.

Well, data centers require a lot of water for cooling. It's harder to pump water up high.

Cheaper and easier, perhaps? If the costs of engineering a tower is more than just buying more land, then why build taller?

It could also be local ordinances. Maybe they can't get permission to build higher than 2 or 3 stories. I know that's common for residential areas; it might be a thing in commercial or industrial areas too.