The discussion of cooling in this piece is more convincing than I would have expected, but there remains a glaring social problem:

Should we consider orbit to be outside of terrestrial tax jurisdiction?

The majority of the cost of putting these data centres into orbit would be borne by terrestrial jurisdictions. The places that built institutions, funded education, provide medical care, etc. for the people who built these things. The environmental impact of building these data centres and launching them will be paid by those living on Earth's surface.

On Earth, we often fail to recoup many of these costs because of out-sourcing, but at least some other jurisdiction benefits. If a poor country is lifted up by the benefits of out-sourcing, at least some good has been done. If we let billionaires simply blast off and evade taxes, that's a net loss to the societies that made this possible with no benefit to anyone but the billionaires. That's fundamentally wrong.

Space may belong to no one nation, but neither is it true that space belongs to no one at all. The space around Earth belongs to all of humanity. Orbital data centres should pay terrestrial taxes. It's not clear where those taxes should go, but we need to hammer out the laws to make sure they are paid.

You can tax the owners on the profits. (Or the revenue, absent profit, if you want to be punitive.)