Cooling in space does not seem like a hard problem to me. You absorb a certain amount of energy in a given time in the form of solar energy, you should be able to emit that. On top of that, in LEO you are only in solar orbit roughly 50% of the time

It is in fact very hard, and LEO is not "solar orbit". You want your datacenters in sunlight 100% of the time, to not need heavy batteries, which is possible, but cooling is in fact very hard