If you mean the underlying data structures, that's basically what modern filesystems are. XFS, APFS, BTRFS etc are all copy-on-write file systems that use git-like structures underneath. In the same way that git branches are "instant" because no data is actually copied, so too can these file systems clone files or whole trees instantly without copying any real data. You can easily "branch" a directory tree, rsync the results to a remote machine, etc.
I get what you're saying about modern filesystems, and I agree. I guess from that POV I'm saying we could stand to remove some of the layers of abstraction?