The physics aren't the problem, though. You CAN cool the processors provided you have large enough radiators, a really good system for the coolant flow, and hardware that's fine operating continuously at around 100C or above.

That's basically an engineering challenge more than anything else. Also keep in mind that one of the reasons the ISS for example requires rather large radiators, is that humans typically don't enjoy temperatures above 40C for prolonged periods of time.

Silicon chips on the other can tolerate much higher operating temperatures just fine and even short spikes around 100C can be acceptable for some hardware.

The real challenge is getting launch cost down and securing the rights to pollute polar orbits and frequency bands. Sure, there's plenty of room up there in orbit, but much of that room is not fit for purpose in the context of orbital data centres. Frequency bands for up- and downlinks are also often ignored in the discussion.

Basically I don't see the current issues with the concept in the required engineering or physics - that's solvable in the near term.

I find it much more difficult to believe that there's a way hundreds of thousands of satellites can share the same orbit (i.e. polar orbit in a quite "narrow" band of distances from the surface) without causing major issues.

Same goes for frequency bands, as it wouldn't be just one US company doing this, but dozens from around the world, each with hundreds or thousands of sats and everyone needs a share of the available communication frequencies.

Then there's the logistics of getting the satellites into orbit in the first place. Not just the launch cost, the logistics! Fuel, NOTAMS, maritime exclusion zones, launch licences, etc. The concept would necessitate increasing current launch rates by at least an order of magnitude and cost aside, the logistics and regulatory frameworks aren't ready for this.