I can backup my local .git by pushing it to a repository in two steps:
git push --all ~/gitrepo
git push --tags ~/gitrepo
I can back it up
Regarding tar: It saves everything: the config (remote URLs), the reflogs, etc. You might want the reflogs if you accidentally do something really stupid in your repository and your hard drive crashes shortly afterwards. Far-fetched, but tar is easy and it does everything. Use tar for making backups, use git push for making mirrors. These are different kinds of tasks.
Regarding compression: I have a 27M git repo, almost entirely plain text, and the .tar.gz is... also 27M. That's not a whole lot of savings.