However, the only advantage listed in this announcement is "near-constant sunlight". It appears they are hoping for 8x solar efficiency for 1000x the cost of terrestrial construction.
If the actual motivation is that people don't want data centers on earth, that seems to be because the datacenters 1) drive up energy costs, 2) use a lot of water I guess, and 3) can make noise. If you're able to operate a datacenter satellite you apparently don't need local electricity, water, or human labor. As someone else said, set up on the desert or in the middle of Alaska somewhere 100s of miles from the nearest person. They can still use solar (just build like 8x the panels if you need to... still cheaper than space), they don't need water, don't need labor... I think most public opposition would disappear.
I've heard some say the real advantage is latency for spy satellites... This seems not a real use case. The kind of workloads that require this kind of datacenter usually can spare 1-2 seconds in round trip time. Millisecond-sensative reactions I would assume would want to be driven by onboard processing.
One true advantage that I haven't seen on any brochure is that the heat produced by the space datacenters could be released into space rather than raise the temperature of the earth. However, the satellite would have to be designed to radiate the heat away from earth. Hopefully they design the satellites to direct the radiated heat away from earth and don't just point the radiators straight back to earth...