?? Git works just fine without any of that. CVS has been around since 1990, RCS since 1982. And SCCS is old enough to be OP's father.
I echo your ??. Sure you don't need a central repository to use git. What does that have to do with suggesting some git hosts that aren't cloud based?
I'm very comfortable with git at the command line, but I still think it's valuable to have a web interface. For instance, with a web GUI I'm able to share a link to a specific line or range in a file in a specific commit.
Typically if I need to do that I'm asking a question or requesting a change, and in that case I want there to be as few barriers as possible to increase the chances that the other person cooperates. Asking someone to clone/pull the repo, checkout a hash, and then view a line in a file is a much higher barrier than asking them to click a link.