What game did you play? (That's not what I saw.)
When developing Fallout, the producer got a call from the marketing department. They were nervous and unsure about the music selection [it was super depressing]. To which they were asked, "Have you played the game?" "Everybodys' dead". You twice mention 'Verdant', but there were no living trees. The world is ruined—no recovery; it's all dying.
The presentation is grim, and only tolerable by the dark humor.
*It goes without saying that to have the world and it's civilization improve or recover destroys the Fallout setting—unless they destroy it all over again; if done that trick will get old pretty fast.
Oh So Cal? Didn't you read up on global warming? Even back in the 90s people were saying it would only exacerbate California's tendencies towards megadroughts, and So Cal being a total desert in Fallout 1 made sense not because of nuclear war, but because So Cal is a desert by it's very nature and probably headed towards even worse desolation by climate fluctuations humans did not alter but probably were actively making worse.
The east coast is by definition a totally different animal. Fallout's environments must depend on what that environment actually is. Environments do not stem from emotional tones. We do not live in a set of fisher kingdoms which is why I take GREAT umbrage to the green tint of Fallout 3 and the desert east coast of the vanilla Fallout 3 and 4 because RADIATION DOES NOT WORK THAT WAY. We know this both from the Chernobyl Exclusion Zone, already verdant and healthy 10 years on at the time of making Fallout 1 and due to the failure of cobalt bomb testing.
To claim artistic license or alternate laws of physics to justify b movie bullshit is simply lazy worldbuilding. If you want similar effects, do your research and come back with better more inventive solutions.
As for human society yeah most humans perished just after 2077, but most of them would have died by 2061 anyway. The issue at hand was society was steadily pulling itself together even in the great shitheap of a nearly waterless Southern California. Junktown, Shady Sands, the Hub, and the various settlements of the Boneyard are thriving or somewhere close to them, and except for the outside of the context problem of the Unity do not need your help in any way to set all things right.
So an east coast would probably be doing substantially better because there's more agriculture, more freshwater, more navigable rivers. See there are two basic kinds of westerns, by terrain, the westerns of the plains and the deserts, that deal with classic cowboys, and spaghetti westerns tend to be those, and the westerns of the forests and the mountains and the rivers, and those tend to be westerns like Maverick, Last of the Mohicans, the story of Tecumseh, the Hateful Eight, etc. An Eastern Western, even one set in Boston, whether during King Phillips War or a war with the Institute can only be a western of the forests mountains, and rivers, but southern New England has two of the three in spades and if you need mountains, Vermont and New Hamshire are a loogie off a skyscraper away.