But like what you're getting at, we already have concepts like "branch" and "undo" and "version history" and "publish" for other uses of the save button and most of those already have their own, more intuitive icons. So why not do away with "save" as something that has to be done manually and emphasize those other actions with their own buttons.
Yes! This is definitely something the user shouldn't have to care about.
I used to have vim autosave every time I changed focus. This worked really well, until I edited something which wasn't in revision control. That time I just cancelled the experiment, but maybe I should restart it and just autodetect if I'm in a repository or not.