I get what you mean, I think what I'm pretty stuck on is what is the centralisation solving? Federated messages dealing with lots of things flowing back and forth and live updates, etc is one thing - but what is it about GH that makes much of a difference when things are in one place or many? Much of the work is done in very isolated sections.

Imagine each organisation/user was run with completely isolated data, and you used something like google sign in for auth (so one global sign in, then oauth).

What wouldn't work? Global search, that I get. I struggle to think of other things though. Maybe whether links between issues across orgs updates? Every commit, diff, code browser, permissions for writing, reading, org level search, stars, would work with zero federated sort of search-y things. Package management, issue tracking, all that would be the same.

Forks followed by PRs? Not sure that would be much different - maybe you'd have to raise an issue on the original project with a link to your new repo & branch.