You literally just need to be in space, because no typical laws apply if you are there. That little detail outweights all sorts of costs.
So, yeah. There will be datacenters in space. Probably unlike any on the ground. Smaller, very likely not running typical datacenter stuff, weirder, operating on a different set of regulations.
If we're lucky, it will be like Antarctica (research focused, still disputed but not armed, probably not lots of shady stuff happening there, costly but still pays off to be there).
That makes no sense. Unless you are going to use the data in space (what for?), you need to import it into a country, and it is at that point the crime will have been committed. You can't, for example, circumvent GDPR laws just by sending the data into space first.