Git repositories do have a full copy of the codebase (unless using some large-file management, same issue with largefiles extension for hg).
But gitlab/github are more than just git repositories -- issue tracking, discussions, wiki, etc. One version control which includes most of this as part of the repository is fossil, http://fossil-scm.org
Really? I find that hard to believe, but it makes me glad I use Mercurial if that's the case.