I'd say it is, in that without it there probably won't BE any narrative after the end of the battle, as there'll be no party left to narrate about.
Eh, while 'classic' D&D seems to have persisted in encouraging a very final interpretation of 'character death' (defeat in combat) long after it stopped always serving the agenda, modern games don't suffer from that problem so much. I mean, sure, if the whole framing of the thing is "lets stake the lives of our characters on success, we'll hold nothing back, success or death!" then they're ASKING for death! So give it to them!
OTOH if they're maybe NOT asking for death then there's always logic in a parley. I mean, MOST bad guys are not averse to ransoms, slavery, etc. You can always kill 'em later. A GM can EASILY come up with a frame for a post-capture type of scene. I know the old, "you wake up some time later" thing is perhaps a bit old and tired and you don't want to use it constantly, but once the PCs are cornered there's nothing stopping them from tossing down there weapons, perhaps in a "we'll spare killing a whole bunch of your minions if you take us prisoner and let us live" kind of thing.
So, meh, I'm not sure most battles MUST be life-and-death struggles.
Which to me shows an advantage of a more DM-driven game: the player doesn't have to bother with these considerations but instead can just play her character and in so doing declare anything, trusting the DM's judgment to just say 'no' to anything that's out of line or ridiculous.
In other words, if I'm the player here I don't want to have to think on any sort of meta-level about "what's good for the story" or "is this beneficial to the narrative" when I'm trying to get my sorry character out of a jam...or at any other time, for that matter. And why is that? Because the moment I allow a thought of "what's good for the story" to change anything that my character would otherwise do, I've stopped playing my character as my character and have instead moved into meta-playing.
I-as-player should be able to just have my character do what it would do (or try to, subject to the DM's permission and-or the system's means of resolution), and let the story take care of itself.
Well, its easy enough for it to just be the GM saying "Nope, that isn't possible here!" which is NOT forbidden. I mean, these kinds of games are intended to be driven by "say yes" type GMing, but there's ALWAYS a limit to that! I mean, characters can only do certain things. Your average dwarf cannot just say "I sprout wings and fly away" any old time, and even [MENTION=42582]pemerton[/MENTION] is going to have some serious questions about that! I know it wouldn't fly (hehe) in my game! Actually it MIGHT, if you're level 27 and you appeal to your patron deity to save your bacon in a really important battle! Of course there WILL be consequences... I'd point out that there's a chart for this in the 1e DMG p111 where the guidelines work out that a character of level 15 who has never asked for divine favor before, and has reasonable alignment behavior has a 41% chance of such intervention! (15% for level, 25% for 'serving deity proximately', and 1% for 'diametrically opposed alignment'). It won't happen every time, but even crazy stuff is intended to be possible in D&D.
Point is, I don't think you're really imposing any consideration on the game that isn't already there in some form. Yes, players in a player-centered type of Standard Narrative game should consider the narrative, but that's why they're playing in such a game, right? Players in ANY game have a similar situation, they're expected to play in a way that shows some deference to the character as an individual. They aren't supposed to just commit suicide because it is fun for the player, or assassinate the other PCs just for the amusement of the player. I'd point out that this sort of problematic behavior is all too well known in games! So I would think that pushing the bounds in terms of player authority when they have narrative agency is really nothing surprising or new.
Obviously there may be some people who just don't want to play this way, but IME that is extremely rare. It may take presenting the game in a way that players relate to when they first encounter such a game, but in the form [MENTION=42582]pemerton[/MENTION] is espousing, which is really the mildest form, pretty much everyone I've tried it on just 'got it'. They produced much more interesting and useful backstory, they pointed out times and places in play which they felt related to their character's concerns, and took those concerns as a significant element of play to be exploited for their entertainment. I'm quite positive players exist who will absolutely refuse to play this way, but its not a huge percentage of those I've met.
As for the specific example:
All of these are of course possible; but many could be seen from the player side as being exactly the same as the DM consulting her notes and (with or without faking a roll) narrating failure on the search.
And further, even if a secret door there is illogical a character desperate to find an escape route might not see it that way in the heat of the moment...
No, but I think they'd see the logic in something else. Some sort of 'deus ex machina', an offer to accept their surrender, or the sudden arrival of an ally, etc. is often quite plausible. It might, again, get a little contrived, but that's part of the whole concept, at least in many genre, that the heroes get these sorts of breaks, otherwise they wouldn't have survived as heroes.
And that's always how I look at it, the story is like an old tale that is being retold. You wouldn't even hear it if the orcs slaughtered the PCs on day 3 of their story and roasted them over a fire. Somehow they pulled through. Maybe not every time, maybe the story is about how they died heroically, but something interesting happened. So there must have been some fate involved to pull their fat out of the fire a few times (or not I guess if they're skilled/lucky enough).