As has already been stated, the NCR is more than just Shady Sands, Shady Sands is merely the capitol from which a nation grew. Between the events of the first and second game, the NCR grew, ultimately incorporating small and large pockets of civilization as they did. Those very same civilizations would likely come to share the same laws and customs of the NCR as time would pass. The Shi and Vault City as civilizations (laws, customs, identity etc.), by time of New Vegas, are likely no more. They are probably just like most real life people, that want to go about their day to day lives, not caring what happened a few decades ago. Again, the NCR is not just one city, it is a full blown Nation incorporating the vast majority of three states.
Edit: Now I'm going to go piss and go to bed, because it's 3 AM
I mean I get your argument, I'm saying that Italy was part of the Hapsburg Empire for centuries and remained culturally and legally distinct. Shady Sands was the heart of NCR as an idea and economic ideal. There's no reason to think its component parts wouldn't feel the desire to go it alone after the end of its central government hub.
I'm not saying it did. NCR clearly exists in some form with the "President" and Moldaver both claiming to be its leader.
It's just there's no apparent central government and it has balkanized.
But in-universe it is presently disunited.
But didn't you earlier try to argue that Shady Sands isn't even the capital anymore and it moved prior to the nuking, and that's why the NCR isn't actually gone? Which then shifted to the NCR splintered into several people claiming rightful authority? Now it's "NCR is dead and here's why that's a good thing"?
Yeah, the show says Shady Sands was the "first capital" of NCR. I'm assuming the Boneyard became the capital at some point given the focus on restoring it.
Mind you, if the nuking of Shady Sands was not THE event that brought down NCR, we can assume there's a lot more shit going on behind the scenes too. Perhaps they definitively lost the War in the Mojave.
Edit:
A clarification:
Personal Feelings: I love shitting on NCR. I'm an Independent Courier supporter all the way then House then NCR. I often love talking about how awful it is even though the games always portray it as, at worst, slightly gray.
Show Observations: NCR is being depicted as a lost golden age of rebuilding that seems to have fallen into chaos after Shady Sands was destroyed. People seem still loyal to it as a nation and identity as well as there are multiple factions that seem to claim allegiance to it as well as claimed leaders. Basically, it's not so much "gone" as no longer centralized.
Possibly a collapse of the economy that was already on its last legs.
There's 700,000 citizens in NCR during NV and 30,000 of them die. Which is slightly less than 5% of the population.
That could easily have caused a collapse of government, economy, and cultural unity.
