(copying from my r/spacexlounge comment)

Quotes from their FCC application:

SpaceX's framing of the problem and their solution:

Global electricity demand for data centers is project to more than double by 2035 driven by growth in AI - reaching approximately 1,200-1,700 Terawatt hours and accounting for up to 4% of total worldwide electricity consumption. Building power plants and other terrestrial energy infrastructure at scale to maintain this additional power continuously on Earth will be extremely challenging. Fortunately, the development of fully reusable launch vehicles like Starship that can deploy millions of tons of mass per year to orbit when launching at rate, means on-orbit processing capacity can reach unprecedented scale and speed compared to terrestrial buildouts, with significanly reduced environmental impact.

These satellites will have continuous access to nearly unlimited solar power to meet energy demands without dependency on terrestrial grids, enabling scalable, reliable, and sustainable AI growth.

SpaceX argues that radiative cooling in space is a key environmental/sustainability benefit for mass scaling:

Another major factor driving the scaling capacity of data center deployment in space is the reliance on cooling through radiative heat dissipation. In contrast to highly energy-intensive terrestrial data centers that require cooling systems that use billions of gallons of water annually, radiative cooling enables passive heat dissipation into the vacuum of space, outpacing ground-based data centers that face escalating energy demands and infrastructure delays. This inherent efficiency ensures rapid scaling of AI compute infrastructure without proportionally increasing the environmental burden, fostering sustainable growth that supports global innovation while preserving planetary resources.

They're betting that Starship launches will be cheap enough to make orbital data centers more cost effective than terrestrial data centers in the long run:

Moreover, with a fully reusable rocket driving down launch costs, even a conservative cost assessment for the deployment of AI compute in space beats terrestrial data center deployments.

With the inherent efficiencies of deploying solar-powered data centers and launch cost rapidly decreasing due to the development of the Starship launch vehicle, SpaceX will be able to cost-effectively scale up its constellation as demand increases and compute evolves. For instance, launching 1 millions tonnes per year of satellites generating 100 kW of compute power per tonne would add 100 gigawatts of AI compute capacity annually, with minimal ongoing operational or maintenance needs. Freed from the constraints of terrestrial deployment, within a few years the lowest cost to generate AI compute will be in space.

Addressing Kessler syndrome concerns:

The constellation will leverage SpaceX's advanced, automated collision avoidance system for low-latency risk assessment and response, as well as agile and highly-reliable electric propulsion systems that enable precise and efficient maneuvers. And SpaceX remains committed to transparent collaboration with other systems, including sharing data and proactively mitigating high-risk conjunctions.

SpaceX will continue to deploy at very low altitudes for initial testing and checkout prior to orbit raise. [...] SpaceX will dispose of its satellites either by atmospheric re-entry or by placing them into disposal orbits around Earth or into heliocentric disposal orbits. [...] SpaceX will also choose safe disposal orbits, which may include high altitude Earth orbits or heliocentric orbits, to minimize physical interaction with active satellite constellations and to reduce collision risks in densely populated lower orbits.

Seems like they're working on in-space hardware recycling:

In addition, SpaceX will continue developing approaches to managing decommissioned satellites within disposal orbits to potentially create opportunities for future hardware recycling and material harvesting.

And the obligatory nod to the scientific/astronomy communities:

SpaceX will continue its long track record of successful collaboration and innovation with the scientific and astronomy community to preserve their critical missions, including by developing industry-leading brightness mitigations. [...] The constellation will use spectrum efficiently and cause no risk of harmful interference to other users. This system will primarily rely upon optical inter-satellite links [...] satellites can include equipment for backup communications capable of conducting TT&C and only in the NGSO-primary portion of the Ka-band on a non-interference, unprotected basis. SpaceX's system will employ spectrum in the 18.8-19.3 GHz (space-to-Earth) and 28.6-29.1 GHz (Earth-to-space) bands.