We have a "community" account here (not an organization): https://github.com/stackmma. I set it up 4 years ago in this answer and uploaded a partial work of mine there (stylesheets). My original vision for this was:
Long term goals of this project
I think the stackmma account can eventually be a place for us to
- host community developed projects (if and when we do)
- host notebooks and snippets for blogposts
- host data files/notebooks, etc. for questions (only in the rare and non-localized cases when a minimum-working-example is not illustrative enough).
We also tried using it for hosting data attachments in questions... but that didn't catch on either.
In the end the idea fizzled, much to my disappointment. Not one person (other than the ones I added initially) has reached out to request to be added as collaborators. I'll admit that I didn't publicize/evangelize this as actively as I could have either.
Is this still a good idea?
It is very easy to convert the community account into an organization. However, for all the benefits that you list, one big disadvantage is that it adds an additional overhead of administering the organization. I've administered a couple of Github organizations (one at work) involving users with diverse skills & git knowledge for almost 2 years now and I can tell you first hand that giving everyone write access to all repositories will lead to chaos. Who will be responsible for taking ownership of a specific repository, responding to issues, pull requests, etc.?
Without good git discipline, sound software engineering principles, familiarity with collaborative development using pull requests and issues, etc., a Github organization will not work. These are things that are fundamentally lacking in the Mathematica community (evidenced by the many popular packages/repositories that have 1, maybe 2 authors max). If those are the traits that would make collaboration better in this community, then we probably don't need a Github organization... you can always fork and collaborate with repos on personal accounts.
In any case, that's just my 2¢. I don't want to stand in the way of any initiative that you might be interested in trying out though, so if you're definitely up for it, I'm happy to turn the account into an organization and make you an admin.