There is uzbl-tabbed, which separates the browser proper from the tab manager. It is not the OS which manages the tab though, since most WMs don't support hierarchal layouts and having all websites along with other applications is quite a mess.

I have always wondered how smooth the workflow can be with a WM that supports hierarchal layouts and tabbing (e.g. i3wm) and having the browser always opening up windows, but I have never done that experiment.