Suddenly the idea of having a CA hosted in space on a satellite issuing certs seems like a good idea.
You're assuming that satellites are exterritorial. They aren't, they're ab initio the launching state's property and responsibility, barring other agreements to transfer them - and getting one out into a "legal void" isn't going to be trivial.
Over the centuries I am sure there will be random satellites that are defunct that will be hacked or otherwise "taken over" by someone with the right skills. These things are tiny compared to the distances involved and in the future you might end up using them as data reservoirs since in many cases it will be cost prohibitive for any authority to go collect or otherwise stake authority over an old piece of hardware considered junked.
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A ship in international waters with satellite internet connection would be much cheaper, except it runs into the same problems as described by the sibling comment: https://news.ycombinator.com/item?id=48469397
You don't get 1,361 W/m² of continuous free energy when you're Earth bound and all those pesky water molecules.
> free energy
It is free only if you ignore the cost of getting the thing into the orbit in the first place.
Edit: also, AFAIK, normal microchips (without special radiation hardening) don't last that long in space
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New startup idea: Starlink for TLS.