Why do Sublime Text 3 Themes not affect the sidebar?

You are looking for a Sublime UI Theme, which modifies Sublime's User Interface (e.g.: side bar). It's different from a Color Theme/Scheme, which modifies only the code part of Sublime's window. I tested a lot of UI Themes and the one I liked the most was Theme - Soda. You can install it using Sublime's Package Control. To enable it, go to Preferences >> Settings - User and add this line:

"theme": "Soda Dark 3.sublime-theme",

Here is a printscreen of my Sublime Text 3 with Soda Dark UI Theme and Twilight default Color Scheme:

You can manually change the sidebar style by editing Default.sublime-theme.

To do this, edit the “sidebar_tree”, “sidebar_heading” etc., classes in Packages/Theme - Default/Default.sublime-theme. You can override those defaults by putting this Default.sublime-theme inside the Packages/User folder.

From the Sublime Text menu, selecting “Preferences → Browse Packages…” will take you to it.

The most recent version of Sublime has fixed this issue, click on Preferences, click on Theme select Adaptive.sublime-theme. This will change the sidebar to a dark colored background.