While the world is doomed, the Capital Wasteland has a fairly good chance to succeed in restoring itself if the Lone Wanderer is good. This is because of several factors.
+The Water Purifier will allow for increased population as people aren't dieing from rads as often. This will also lead to more skilled people being present and also more skills to be had as the general knowledge available increases due to longer lifespans.
+If you increase Herbert's growth then the land may be terraformed in a few centuries creating a very valuable amount of resources for the people of the wastes to tap into by creating a larger and more expansive ecosystem.
+The Lone Wanderer being as dangerous as /she is, has probably come into conflict with Talon Company, Slavers, Raiders, and Super Mutants. While s/he may have not destroyed them, the sheer amount he has killed by endgame will have weakened them. This will provide the variety of factions they prey on time to grow, making it harder for them to being raided. In turn this lets them preserve more resources, which increases further growth until finally these destructive factions are but nuisances.
As you can see the Lone Wanderer is an amazing factor in the restoration of the Wasteland. Any faction s/he joins will have decisive advantage in becoming the founder of some new Capital Wasteland government. Hell if the LW wanderer has connections with whoever is running the Pitt, they may just create a state somewhat like the NCR.