I figured someone would respond with something like this, and I considered writing in expectation, but I was lazy.
The issue isn't that these factions have collapsed. It's why they collapsed, what remains of them and what has happened since. I hope my tone in this comment isn't harsh, it's not meant to be. It's just tv, its just for fun and I enjoy these kinds of discussions^[most of the time. I can get too invested when things get heated, but that's not enjoyable, that's just a bad habit. I hope we both assume the best of the other], so I hope this is received as us just talking shop about slop.

nuking their capitol is hardly just a village

I agree, but what was depicted was just a village. Even if it was shown to be a metropolis, it still wouldn't make sense. If California was it's own post-post-apocalyptic nation-state, then bombing Los Angeles wouldn't destroy it, even if it was struggling logistically. The game spends a lot of time detailing the many factions within the NCR and their interests. They don't disappear just because the government is in a crisis, nor if the government disappears. The new world capitalists like the Brahmin barons and the caravan companies don't just go away.
Army Centers, logistics hubs, supplies and so forth do not just disappear, which is what has happened practically. Even if the NCR somehow was destroyed by nuking what is, at best, a suburb, then that still doesn't mean it goes into thin air.
The game also touches on this with Lonesome Road, where you are given the option of nuking the factions. It's made clear this will cripple them, stop them from expanding, perhaps force a reconsideration of method, but not just wave a magic wand that makes them go away.
Likewise the game makes it clear Caesar's legion will splinter with Caesar. I don't mind that. I do mind that the massive nationstate is reduced into two tiny camps that border each other. Practically that is what can be shown, maybe, but narratively too? That is my issue.
The NCR is shown in-game to be struggling massively yes. It is also shown to be massive.
The creators of the show manage to show and consider this scale when it deals with the BoS, but it goes completely out the window with any New Vegas faction. That is my frustration.

I can see what the narrative does with the destruction of these factions and appreciate that, but I don't see anything that makes these factions into anything recognisable from the game - beyond aesthetics - which is why I am wondering why they didn't just make up their own new-world government/raider faction if that's what they wanted.
That confusion ties into my general frustration with Bethesda-fallout that seems to have a hard time making new things and letting go^[DEAD MONEY REFERENCE? POG. YEAH ITS ABOUT LETTING GO. LETTING GO OF POVERTY] of the old.

Edit: added footnotes and a little extra in the end

double edit: Gonna go back and watch this ranger vs BoS fanimation to cope I was looking for a specific edit of it but what the hell. Also here's Caesar getting looney toons'd