In this case, I think that the leading Git provider is where it should be hosted, due to community size. And that's GitHub for now. That can absolutely change in the future.
Git was created to be distributed. Endorsing an account-required, closed-source platform is not the best play for Git as platform (nothing wrong with it having accounts, and the account providing an improved experience). IMO, it is important regardless of what platform's in vogue to use a more generic term here.