"Thermal management, or cooling, also presents fewer challenges in the vacuum of space compared to Earth."... this is false. 

We have 3 options for cooling: conductive, convective or radiant. On Earth, the last is almost never used because it is the worst of the 3.In space, it is the only option. 

Radient panels exceeding the sizs of the Internationam Space Station, currently the largest orbiting structure ever built, will be needed for each data center. A similar array of solar panels will be required for power. These are not trivial problems, and Space X has shown no ability to launch and construct such massive infrastructure yet. 

Then there is the short orbital life of LEO satalites, which would require refuling. And the issue of sever maintenance. Would technicians be required to repair items on space walks? Or would a pressurised maintenance craft be launched to allow the to work without needing to suit up? Or will robots be used to tele-operate repairs? Who knows. Not Musk so far as I can tell.