Very interesting idea, I’ll consider adding something like this.
For what it’s worth, you could use CSS for this at the moment:
You can hide tabs by right clicking the toolbar and hitting “Show Editor Tabs”.
Be sure to also check out the customize mode; right click toolbar > Customize. In this mode you could combine the Open Files Widget with the Places widget (so they are stacked vertically). I tend to use Komodo this way myself.