This objection is far broader than you here claim. Heroes of fiction also don't die ignoble deaths at all, but only at narratively important times. They also don't fail except in cases that having a setback turns out to advance the story. In heroic fiction, the reader generally has an assurance that the protagonist will win out in the end and the characters generally have some sort of plot armor that protects the story from ending in an unsatisfying manner.
Or as the kid in the Princess Bride says, "What, you mean [Prince Humperdink] wins? Grandpa! What did you read me this thing for?"
I think it's obvious that D&D and pretty much any RPG first written before 2000 is not trying to emulate that sort of assured outcome. The player is given every opportunity to fail, and while the game is generally balanced to allow the outcome of victory it's by no means an expectation that the PC will not die ignoble deaths. Indeed, there is in historical D&D an expectation of a lot ignoble deaths.
I don't know that that is entirely the case. In "The Lord of the Rings" in the climatic passage of the story* where Sam and Frodo discuss the meaning of stories on the path of Cirith Ungol, Sam observes that in realistic fiction it's not the case that the protagonists have plot armor or always make the right choices, but rather that stories are sifted by the audience and we remember the protagonists who made the hard choices and carried the story through to the bitter end, whether or not this bitter end was a heroic or tragic ending. Plenty of stories occurred other than these stories and had heroes who had ignoble and undramatic ends, but we choose not to tell and remember those stories because they are unsatisfying. I think D&D classically worked like Sams sifter of stories, where there were many possible protagonists who failed and died ignobly but that we carried on the story with the ones who did not. Protagonists were always replaceable. There we no guarantee you'd earn a noble death or a heroic victory with this protagonist, but you could roll up another one and try again.
*(In Tolkien preparing for the battle is always the actual dramatic climax, and the battle itself is almost always dramatically anticlimactic and resolved with a twist, often with the protagonist not even being the primary actor in the battle. It's preparing yourself to "go over the top" and "do your duty" that is for Tolkien the truly heroic moment.)
So yes, there is a philosophical difference, and we have more and more seen games written since the 2000s that have tried to make a game where the PCs do have plot protection and can't die except when it is dramatically appropriate to do so, but if you bring that into your game I personally don't think it solves the problem and guarantees you create a narrative that resembles heroic fiction. One problem is often that you aren't creating verisimilitude. In a good story, the author comes up with skillful and clever things for his protagonist to do so that their success, however much it is in reality because of plot protection and because as Stan Lee says, "because the author wanted it that way", the audience feels like the victory is earned. And if the audience doesn't feel like the victory is earned, they groan, they lose their suspension of disbelief, and they say, "Arrggg, this is a bad story."
I think therefore that ultimately both groups are trying to emulate heroic fiction in their own manner. For Gygax and other traditional RPG authors, it's the responsibility of the player to emulate the actions of heroes through what he calls "skillful play" and thus earn the outcomes of heroic fiction by successfully navigating challenges in the way heroes do. Gygax doesn't put this burden on the system or the GM, whose role is to sift out protagonists that don't have the moxie and cunning and heroic will or character to succeed. The Narrativists are trying to provide a framework where plot armor exists to guide the players to satisfying endings, but they are in my opinion just as dependent on or even more dependent on the players providing that "skillful play" that Gygax wanted if the framework is to generate satisfying stories. It's just, I don't think the authors of those Narrativist games are typically as aware of that fact as Gygax was, nor do they seem to think that ignoble ends are fun whereas Gygax seemed to think that the "journey along the way" was as fun as the destination, or at least there was no way to rush it. I consider Ron Edwards complaint that he never got there a huge part of the Narrativist movement and why (hitherto) I think it has failed ignobly (in as much as the majority of people have never adopted Nar assumptions of play). I think this is because for all its striving, as of yet, Nar isn't actually "getting there" in the sense of better more enjoyable plots and transcripts of play more often that Trad was.