One solution is to put them in space, leaving more room and resources for humans and wildlife.
Such structures would have better latency due to locality, they wouldn't be subject to transmission interference from weather, they'd be far more accessible for replacements/upgrades, and being underground naturally aids in cooling and noise suppression.
While it would be resource intensive to dig out the underground structure, I'd be surprised if it even came close to the resource expenditure required to launch all your computer hardware into stable orbit, not even accounting for the fact that the former is a one-time, up-front cost, while the latter would have to be re-done every time you replace hardware.
First, getting them up there.
Second, disposal of them when they reach end of life, which is about 5 years.
The difficulty with getting them up there is we currently don't have orbital rockets that don't cause tremendous damage to the upper stratosphere. It has been tolerable so far because we've only done about 7500 orbital launches over the history of spaceflight.
The more extreme plans, like Musk's for a million data centers in space, would require around 10000 launches to get them deployed and then as they age 2000 launches a year to replace old ones.
There is active research and development on rocket fuels that won't cause massive damage, so this problem may be surmountable.
Reentry at end of life is also a concern. As they burn up they deposit things in the upper stratosphere that we really don't want there. As with launches that's not been a problem yet because over the entire history of spaceflight there have only been about 10k satellites and rocket bodies that have reentered, plus about 25k small things like debris.
That would be around 200k per year under the million data center in space plan. I don't know if it is possible to build them so they don't cause problems on reentry.
Probably a better approach for now is to build them in places where large power generation projects are being built. Those projects are already adding new power transmission capacity to get the power to cities, and it should be fairly efficient to at the same time add massive fiber internet capacity along the same right of way used for the transmission lines.
This is an idea that is getting a lot of airtime but not sure if anyone practical minded thinks it is viable in the next 15 years.
1) You must have access to the core of the power grid, or a local very large power plant (that can't be near the end of its life), because elsewhere you can't get megawatts of power, never mind gigawatts
2) You need access to year-round flowing water (mostly because of regulations, or without regulations it would be possible to deal with the problem without access to a river)
3) You must have friendly government, banks, ... with realistic promises of staying stable for decades (because of the investment required) (this includes stable interest rates, and yes, despite Trump's best efforts, US is still on the top of the list here)
4) unless you're a hyperscaler that can pay for burying hundreds of miles of fiber, you need to be near crossing points of long-distance fiber links.
5) You must be within 10-50 milliseconds of what you're going to use them for (which, granted, is not much of a restriction in Europe, but it does mostly exclude places like, say, Africa, Australia or South America)
This means that even inside the US, the places where you can build a datacenter are small dots across the map, and there's only several hundred of them, not thousands. The only imho realistic way to make these things be located elsewhere would be to revisit the water regulations a year ago, because it's one of those things that doesn't really make sense anymore.
It was never a serious proposal, it's just some zillionaire's daydream about having their own Neuromancer-style space-station, a place where their word is law and their dynasty assured by a pet superintelligence.
The only "data-center in space" we're likely to see will be tiny low-power satellites, offering themselves as extraterritorial hosting (i.e. actual data, versus processing) for stuff like an oligarch's ill-gotten crypto-currency.
Yeah, Jeff Bezos gives it some lip-service, but that's to promote Blue Origin as a company to launch rockets. Somebody will probably launch a symbolic little temporary thing to claim the prestige of "first datacenter in space".
But beyond that? Nobody's planning exaflops of compute in orbit, if they're sinking deep investment in satellites at all, it'll be for their classical role of relaying (or collecting) data.
If the issue was "leaving more room and resources for humans and wildlife", it would be much cheaper and easier to put DCs into the ocean. Yes, it's a hostile environment for such hardware, but it would still be much cheaper to handle all the downsides for the same amount of compute - including maintenance, which is currently economically impossible for DCs in orbit.
one of the biggest threats to AI accelerationism longterm is the public rioting or foreign governments launching attacks against data centers
the plebians won't be able to burn the data centers if you put them in space though.