I mean if you're going to say when everything went to shit from 2277 to 2282 (when Todd said the nuke happened), then that's as good a time as any. The Legion, economic collapse, the destruction of the Divide, and other shit all happened in a relatively short period of time.
Technically Todd didn't say that 2282 is when the nuke happened, he just said "It happened shortly after the events of New Vegas", probably because both Todd doesn't know exactly when the nuke happened and he doesn't want to be pinned down on some specific years since you could poke further holes and argue it invalidates some end slide or other if events transpired within a month of the game ending (given the game starts in mid-to-late October, it seems not a stretch that the game would actually end in November, December, or even further into 2283)
No...because when an empire "falls", you talk about the beginning of the descent into things.
Fall of Rome
Fall of Byzantium
You know, history.
What you're describing is not how the fall of nations are talked about.
I don't know how much of a student of history you are, but... both of the terms you cited are most often used to mean the actual final capture of those cities as a virtual end point for their respective polities. The Fall of Rome most often refers to the capture of the city of Rome by the Goths in AD 476, and used as a marker for the end of the Western Roman Empire.
The Fall of Byzantium is admittedly a little less conventional given that the polity is referred to as the Byzantine Empire or the Eastern Roman Empire, and the city is referred to as Constantinople, but given that Constantinople was originally called Byzantium (and that is where the historiographical name of the empire comes from), one would most obviously take this phrase to refer to the fall of Constantinople at the hands of the Turks in 1453, used as a marker for the end of the Eastern Roman Empire. And indeed, the first five google results that turn up when you search for the "Fall of Byzantium" are the fall of Constantinople, not the decline of the ERE more generally.
"The Fall of ___" can be and is used to refer to longer and more general processes of decline, but it's plain and primary meaning is the literal
fall of a city, a siege. If you wanted to refer to the decline of a polity, of an empire like the Western Roman Empire or the Eastern Roman Empire, you would refer to that polity rather than its capital city, and indeed this is how people usually refer to these things.
In the case of "the Fall of Rome", most often in my experience it refers to the fall of the city itself in 476, but since the city is synonymous with the empire it is sometimes used to refer to the state's decline more generally. We could use fall of Byzantium the same way since Byzantium is a historiographical term with some ambiguity, could refer to the city or state. One trouble with drawing an analogy to the fall of Shady Sands is that Shady Sands is
not synonymous with the state, the New California Republic. Though maybe it would work if the blackboard was referring to the decline of the State of Shady as a whole... though given that Shady Sands has been moved to LA, it's not clear how the State of Shady could exist at all.
It's not inconceivable that the 2277 mark refers to something other than the nuke (indeed I don't think the writers intended it to nesescarially in the first place), but it's an odd locution.
