1st of all lets clarify: What you mean is the statusbar. The gutter is the area where line numbers are printed.
This was the reason why I was wondering what you mean.
2nd: I like the idea to be able to interact with certain areas of the statusbar, too.
3rd: I agree with @davorin. The only thing VSCode does when clicking the statusbar icon is opening a command panel to perform the underlying operation. This is what GitSavvy can do for you, too. For many commands, you don't need to open one of the dashboards.
Just open the command pallet and enter
git:. You'll get an overwhelming amount of commands offered, which work without changing to another view or window at all. VS Code doesn't more in that case.
git: stage current file and commit
If you miss a command, you can even create your own custom command and place it to the panel.
What I like with VS Code is the list of modified files as alternative to the normal tree view.
some people might want to have support for Subversion or Mercurial
This is a question of design. While ST packages tend to be specialized hobby projects for certain use cases, the guys behind VS Code at least seem to try to create a commonly adaptable API and infra structure. Therefore they create
language-server-protocol to make very common interfaces available, which can be used by devs to support different languages, version control systems, debuggers, etc.
But these kind of developments require a large team of software architects to create and maintain a proper design. This will hardly be achieved by some hobby devs, even though I'd like to see something like that for ST, too.
ST core basically comes with the features required to build such things. But it would require capable and willing devs with enough spare time to make use of it the same way VSCode does.