No idea, but Google groups are central to the Julia community. Guess they just like to use google. We could fork it and do another login if we wanted to escape google.
https://github.com/JuliaLang/JuliaBox
Google was just for convenience and something to start with (and not worry about user management). We also want to be able to use the Google Drive Sync. Once we sort out other pressing issues, we will certainly add other methods to login before announcing again. Pull Requests are welcome too!
Google Groups were just convenient when we started, compared to other mailing list software. It is not the greatest, but better than most other things out there - and gets the job done.