Bazil has similar goals, but wasn't ready enough for me.
I do very much like sibling /u/pritambaral's suggestion of OwnCloud support. I tried OwnCloud briefly in the past, but ended up switching away. A feature like this might get me to try it again and stay.
Yes, because everyone knows it would be amazing to have this kind of functionality just work for everyone, regardless of their personal OS and technology/device choices.
A couple days ago I contributed https://github.com/DanielDent/git-annex-remote-rclone to git-annex, so in theory you could use Dropbox as a backend for git-annex if you wanted to (I haven't personally tried it with Dropbox).