I’d start off by pointing out that the game being played is a huge factor here. What the players are allowed to narrate affects how much narration is necessary and acceptable.
Yes, but when you say "the game being played", do you mean the system and rule book? I am not aware of any difference between 3.5 or 4E rules on player narration versus 5E rules on player narration, because I'm not aware of *any* rules in 5E on player narration. There is some tradition and culture, among D&D players, which interacts with the rules as written, and which varies from table to table. Hero System has a genre-specific rule about player narration *in character*; when you're using Hero System to play Champions, you can establish that *in-character* monologues are Zero Phase actions (equivalent to free actions). Hero System doesn't have RAW about out-of-character player narration. (Well, not as of Hero 4E.)
Universalis has rules for what players establish about the fiction. It does not have rules for what players say when speaking in the voice of a character; the declarations which spend Coins to establish Facts are out-of-character. (Universalis is a no-DM system.) I have only played Fiasco once and didn't read the rules book, but I gather that Fiasco allows quite a bit of player narration, including narration which establishes facts in the fiction.
Having said that, generally speaking, I find high levels of player narration to be annoying. I don’t mind a bit, and I certainly like when players are engaged and talking about the situation. But when it’s a player’s turn and they start in with something like “Recalling his days on the high plains of Valinor, the stoic ranger Aspar presses on, undaunted by the challenges ahead...”
I find that self-indulgent. I imagine that player writing novels which are Mary Sue homages to the awesomeness of the protagonist. How about player narration which isn't a zoom onto the face of that player's PC? For example, a narration in which one PC turns attention towards another PC - "Aspar sprints to the side of his fallen comrade Lavinia, to see if she yet lives" - which is meant as a set-up for either the DM, or Lavinia's player, to narrate Lavinia's status? (It's possible that the GM doesn't know Lavinia's exact progress along the Wound Track; so the GM might turn to Lavinia's player for further narration.)
You mention "it’s a player’s turn". In my experience, gamers apply rigorous standards of "it's my turn, now it's your turn" more during combat (or chase or other action scenes) than during most non-combat. I've also experienced (recently) wrangling over who's taking too a long turn, when PCs enter a village, and split up to pursue a variety of non-combat downtime goals. The dwarven paladin went to the local smithy, the sorlock sought an appointment with the local mayor, the rogue found the worst bar in town, and the DM spent some time on each of their conversations with NPCs. Those scenes aren't mediated by the combat rules; they're not in initiative order as modified by DEX; they still raise the question of which player gets how much of the DM's spotlight. And in all those scenes, one of the time factors, is how much the DM narrates to establish facts and tone about the smithy, the mayor, and the dive bar. If the dwarf paladin's player goes to the smithy, and the DM spends five minutes describing the smithy then five minutes of NPC in-character speech, the local smith telling the story of how he was once an adventurer before he took an arrow to the knee, then that's ten minutes of that scene, before the player has a chance to say *anything* about what he wants at the smithy. If, at that point, the rogue player gets itchy - "when can we resolve what I find at the bar?" - then that player's impatience is understandable AND the paladin player might feel caught between "I want to play my PC!" versus "my scene has gone on too long already".
Wait, what does any of this have to do with literary value?
IMO a story in which the PCs *each have their own interests*, in which the paladin's interest in the forge comes from his worship of Tharmekhûl, while the sorlock's actions follow from his Noble background and his membership in the Lord's Alliance (plus he's the high-CHA "Face" of the party), and the rogue goes to the dive bar *to differentiate himself from all these lofty heroes he tags along with* (he's in it for the loot, not the heroism), is a story with more potential for literary quality, than a story in which the PCs stick with the trope of "go to the local tavern and flirt with barmaids".
This potential for literary quality comes from the players, not from the DM. But whether this potential gets realized, or not, depends in large part on how well the DM rises to the occasion. If the DM has a pre-written speech in which the mayor has a side quest for the party, and thus the DM spends time only on the sorlock's visit, while dropping the ball or giving token attention to the visits to the smithy and the dive bar, then the DM is missing an opportunity, and the DM is rewarding one player with more spotlight time than the others.
In this situation, perhaps the sorlock player should interrupt the mayor (and thus the DM) with "Hey, I came here because I've discovered clues indicating a regional threat, which I'd like you to communicate to the rest of the Lord's Alliance. If you have a mission for my party, then how about I gather the rest of them, and you tell all of us at once." The sorlock might, in the process, lose the scene the player hoped for; and the player will discover, if he doesn't already know, how well the DM responds to narrative interruption.
