I suspect that Musk wants to build space data centers in order to mitigate political and societal problems, which may yet prove more intractable than cooling in space.
The current expansion of terrestrial data centers has already caused a huge backlash. Their adversaries may well try to regulate them out of existence, at least locally. If an important jurisdiction like California or Germany subjects building of new data centers to regulations similar to building, say, a new nuclear power station, they will achieve a de-facto stop on further development there even without banning them outright.
Space, while not entirely lawless, is much harder to regulate this way. Local authorities have no power over it, nor do governments of nations without space capabilities. Big authorities of big nations (the FAA etc.) do, but they will likely be more friendly to already established launch businesses like SpaceX, not least because of the geopolitical dimensions of having a vibrant space sector.
From Musk's POV, this may be worth the additional cost and technical troubles.