Providing GPS, communications, media, etc. in space so there is access anywhere in the world has a clear advantage. Here the only pros seem to be that it is potentially cheaper than a datacenter on earth because of solar and cooling. But I assume the environment impact is worse than having datacenters on earth. Launching lots of satellites uses lots of fuel and CO2 emissions. Building satellites and dealing with the end of life tech has much higher environmental impact than dealing with datacenters on earth, where you can do proper waste management and recycle materials. From the economic point of view, polluting the environment is currently free. I guess if the externalities would be part of the equation it would not be economically viable.

Maybe this project exists because the "early in the game" factor. It has worked well in the past for Google, OpenAI, etc. They used copyrighted content to train LLMs to sell AI. They indexed Yahoo directory and websites before robots.txt existed, once they have a dominant position they put robots.txt in Google results so new players can't use their content. And they are launching AI in Space before regulations and politics catch up.