Now, obviously, one may have absolutely no interest in these sort of narrative concerns, and this question would not even be worth considering. You might approach the rules as a framework for exercises in logistics or purely as a game to be won. You might find that, regardless of whether a game's rules are oriented around fantasy, superheroes, vampires, cyberpunk, or anything else, all of this really just boils down to trappings and that "kill them all and take their stuff" tends to be a lot more interesting than trying to emulate genre conventions or to employ narrative principles as rules of gameplay.
There is another option aside from "Story Now" and "kill 'em and take their stuff". I have no interest in narrative concerns and approach my RPGs with an interest in
playing the role of a person in an alternate reality. So explore that reality, find interesting things to do, and do them.
Just like in the real world, if you're doing interesting things, then the experience is interesting. It's also likely to give you a good story to tell afterwards, and, when you tell it, you're likely to use various narrative devices to enhance the story, but, when you're doing it, you (generally) aren't doing it for the sake of the eventual story and you (generally) aren't actively altering your actions to fit established tropes in order to get a "better" story out of it. You just do it and let any stories (or lack of them) worry about themselves.
So is everything leading up to the BBEG fight just basically filler?
Personally, I don't even follow a "lead up to the BBEG fight" structure. There's a place. There's stuff in the place. What the PCs do with it is up to them. It's not "story filler", it's a natural part of the simulated world they're exploring.
And if things do take a bad turn and there ends up being a TPK, do you still find the narrative satisfactory? Do the players? Not being facetious here.
Offhand, I can't recall ever being in a TPK, but it seems like a lot of them generate good stories, given how many people tell crazy stories about times when their character died in a TPK. I have no idea what proportion of TPKs end up that way vs. how many only produce a bunch of pissed-off players, though.
But I can tell you that one of my most memorable RPG experiences from the late 80s was the time that my character was one-shotted by another PC, completely out of the blue. And, no, this wasn't him being a jackass or approaching the situation as "purely a game to be won". On the contrary, it was a good moment of roleplaying - my cleric had just discovered the ghost of his dead ex-lover and was about to destroy her permanently. It made perfect sense in the alternate reality of the game that he would do whatever it took to stop my character and, as a player, I found that it resulted in a very satisfactory narrative, seeing as I still remember and retell the story today.
I have been gaming off and on for over 35 years now, and a series of battles is not going to be enough in and of itself to get me invested in what is going on, even if there is some level of genuine drama purely in watching my characters HP dwindle. Is this kind of formula enough for you to personally feel invested?
No, because your formula left out role-playing. Getting into your character and living in the setting through that character is what gives meaning to the battles beyond simple exercises in tactics and/or dice throwing. (Which is not to say that the battles are at all necessary, only that, if there are battles, role-playing can give them meaning without needing to introduce narrative concerns.)
By narrative I don't mean a hypothetical story that might be told about the game somewhere down the line; I'm talking about the experience of the events as it unfolds. We read a book and experience the narrative of that book. We watch a movie and experience the narrative of that movie. We play a session of an RPG and we similarly experience a narrative of imaginary events.
I disagree with how you're using "narrative" here. The experience of playing an RPG, for me, is not "narrative" in the same way as reading a book or watching a movie. When I play an RPG, I am
there, making my own decisions and doing what I want to do, the same as if it were real. I don't experience it as if I'm telling a story and I'm absolutely not consuming someone else's story about the decisions someone else made. (Incidentally, I
really, really hate fiction which is written in second-person for basically this reason. The character isn't me and I have no influence over their decisions, so don't address me as if I am.)
EDIT: Let me try and give a specific example of what I mean. Let's say that as part of the interesting (to me) world that I create, there is a powerful evil dragon living in the mountains west of the city where the PCs live. The PCs get wind of this dragon and march to the mountains and directly into the dragon's lair. For some reason they thought this was a good idea, but they all end up being killed very quickly by the dragon. Is this a good satisfying narrative? Are there ways to make what feels like essentially a random TPK into a satisfying narrative experience?
Whether the dragon scenario produces a satisfying narrative is all about the context of the events, not the events themselves.
If the players hear about the dragon, say "A plot hook! We must pursue it!", and dutifully march into the dragon's lair to be slaughtered, then, no, that's not terribly satisfying.
If, on the other hand, one of the PCs is a ruler and his lands are attacked by a dragon, then he discovers that the dragon was enraged by a thief stealing from its hoard, so the PCs prepare themselves to deal with the threat before it causes more harm to those close to them, possibly stopping off along the way to settle accounts and say their farewells in case they don't return, and they slay the dragon, but are mortally wounded in return... then you can get a pretty decent (if tragic) narrative out of it. (As evidenced by the fact that this is basically the death of Beowulf, translated into a party-based RPG.)