As noted by @neoh4x0r making the tabs show the whole path will make them too big to fit more than a few.
There are a number of alternativess, as noted by @ralf3u the full path is shown by hovering on the tab, as noted by @neoh4x0r the various tree/file browser plugins show the full trees, and I will add a note that the builtin `Document` sidebar also shows the path to the open tabs.
So its unlikely that another option to show the same info will be accepted.