It's completely possible to take a piece of GPLv2 or v3 software, make extensive changes, and provide it only as a web service without ever being required to make those changes available to the community. AGPL solves for that important case, where if you use AGPL software to provide a service and make changes, in addition to providing the service you must also make your changes available to the community.

But I think I misunderstood your point, you were focused on the GPLv3 itself. Which I don't think prohibits running on any computer as you say.