Cooling is probably the easiest problem to solve, easier than power. And in both cases, the problem is solved by mass to orbit. All you need for cooling is a big f-ing radiator. Solar panels are chips, and not trivial to manufacture. But a radiator is just a hunk of metal with some pipes.
That's why the cost of mass to orbit is the most important thing. You can solve almost any space problem by just throwing more mass at it.
Solar panels are 4x more efficient in space. 2x because of lack of atmosphere and another 2x because there are 24 hours of sunlight in SSO.
Is it really that hard to just say, "I don't know if it will work or not"?
Ridiculous. Have you ever seen a container ship? One engine on a container ship puts out 80 megawatts, or around 80 orbital data centers' worth of power. So if there's not enough room for solar, which would surprise me greatly, then running a generator is not going to be a problem.
As for the lack of 24-hour operation, a ~50% duty cycle is a perfectly reasonable tradeoff for not having to launch something into LEO. You can easily deploy several times as many installations for the same money if they don't have to work in space. And they will be maintainable, to boot.
And I fully sympathize with the need to remove these things from local and even national sovereignty, having seen as an increasingly-horrified American just how destructive populist influence can be.
But putting millions of servers in orbit? That just doesn't seem like the way forward, for so many reasons.
As for weather, OK, fine, whatever. Deploy 6x as many.