My main gripe with Github isn't so much Issues, it's that repos can't be grouped (the closest would be creating a different account per group of repos, but then each repo has a separated Issues and Wiki) unlike at Codebase.
And even more importantly, the pricing per repo instead of storage size makes modular projects too expensive.
Which is too bad because other than those two points, I used to be very happy hosting at Github :/
I think OP's point is this: Consider Google. Google has many projects on Github, including Chrome, Polymer, and Angular. Some of those projects have sub projects (like Chrome Dev Tools or the Polymer Paper Elements). It would be way easier to browse those repos if there was some hierarchy or tagging mechanism to them. Instead, there is only the org.
Therefore, you end up with a single large company or project balkanizing itself into many orgs simply for organization's sake. This, in turn, makes administration and anything else that crosses org boundaries cumbersome.
To be fair, it's not a problem that most Github projects (or even most popular ones) have. But, I think the issue the OP is raising is that orgs only let you group projects at a single level, which makes things hard to organize in a world that's moving to lots of tiny repos for what may have once been a single codebase.
The separate Issues problem could be worked around by disabling Issues on all repos, then creating a new “our-org/our-project-issues” repo that contains no code, but has Issues enabled.
And even more importantly, the pricing per repo instead of storage size makes modular projects too expensive.
Which is too bad because other than those two points, I used to be very happy hosting at Github :/