Great post, and I agree with most of what you said, but I don't know that I agree that The Wall is definitely 100% going to repel the army of the dead if they never get a dragon (through Jon's bumbling fucking idiocy of a plan, which may be the single worst plan anyone on the show has ever had; how the fuck did he plan to isolate a single wight in an army of tens of thousands? It's not like they step away to take a piss. It's just mind-boggling that anyone went along with it). If that were the case, why bother manning The Wall at all? If it's solely to keep the Wildlings on their side, then already the idea that "all men must stand against the army of the dead" is shattered because you've effectively said "except for y'all, we don't care if you die and bolster his numbers, we've got this huge fuck-off wall to protect us." They man The Wall because there is an expectation that whatever magic is imbued in The Wall is not going to be enough to prevent the armies of the dead from eventually penetrating it.
Now, again, Jon's stupid fucking plan accelerates everything by giving the Night King a really easy path through The Wall. No doubt they would have been better off having not done that. But the Night King, despite spinning his wheels for fucking decades taking Craster's kids and just sort of staring at The Wall wistfully like "one of these days," has also accelerated his plans through the attack on Hardhome. That, plus all the Wildling corpses he keeps stumbling across, bolsters his strength to the point where he's going to attempt to breach The Wall irrelevant of whether he has a dragon. And we keep hearing that the Night's Watch doesn't have the men to repel him, even with this so-called "Wall Magic" that's supposed to keep him out. So even if he doesn't get a dragon, there's a solid chance he takes Eastwatch regardless. And it's not like you can weaken his army by lessening the number of soldiers he has; after a battle, he just resurrects everyone, plus the dead on the other side. So, effectively, every single battle his army gets more formidable.
So you have to accept that he's going to breach The Wall and start moving south, killing dudes and building his army; this has been the internal logic of the show since episode 1. Even barring Jon gifting him a dragon, this was inevitable. If the characters do nothing, as you claim, then the Night King takes over castle after castle, killing everyone and building his army until they are an unstoppable force. They pretty much already were; they took out the Dothraki instantaneously, as well as the Unsullied, and pretty much killed everyone in the castle outside of the people with plot armor so thick it stretches across the narrow sea. If the characters do nothing, instead focusing on war with Cersei and King's Landing, they're still going to have to face the army of the dead, except it will be 200,000+ strong and they'll have very few soldiers left due to their war for the Iron Throne. They couldn't just ignore the issue. Cersei has more of an excuse because she's over a thousand miles away while the North is the first thing that's going to be hit geographically. But the idea that "just don't worry about it" is somehow a valid response to the threat that the Night King represents doesn't make any sense whatsoever. They have to respond in some way or the North gets flattened, and the rest of Westeros follows with it.
Now, that being said, I think that you're absolutely correct in the rest of your assessment that the way the show handled the particulars ultimately made most of the other things we've seen pointless. It does ultimately subvert the narrative because the South had to offer nothing and they won't even believe the threat was ever real, the North lost most of its fighters while Cersei bolstered her strength, and the threat was defeated in a silly manner. But the North were sort of fucked here regardless. It echoes the Wildlings asking the Night's Watch for help and being told to fuck off; they aren't here yet, not our problem. Which actually seems to be a recurring theme in the show; "why the fuck should we help you... oh shit, please help us!" Cersei's biggest win here is a matter of geography more than anything (that and treachery, but we're used to that).
