I think that would be just a short-term solution to the real issue: a better overview and navigation of your tabs in larger-sized projects.
We have projects at work with +30 tabs. Hiding any of them would not make sense, as you often need to jump between them. That is really painful at the moment, even with the new search box. (I can give a more detailed description of our use case, if anyone is interested)
A tab list that uses the vertical space, that is always visible and scrollable by mouse wheel would be a great improvement for usability in these cases. Preferably that tree hierarchy view that @knolleary had mentioned in his earlier post. 
