D&D, and 5e, also has a traditional play loop. The three-step process is described in the 5e PHB on page 5, under "How To Play":
"The play of the DUNGEONS & DRAGONS game unfolds according to this basic pattern:
1. The DM describes the environment. ...
2. The players describe what they want to do. ...
3. The DM narrates the results of the adventurers' actions. Describing the results often leads to another decision point, which brings the flow of the game right back to step 1."
Heavy abstraction here--and not entirely accurate either. Players are frequently invited to describe environment (as you yourself note later on). DMs often prompt for actions, or even specifically instruct the players to do something, e.g. "make a Perception check" and "roll Initiative" are both incredibly common. Finally, players don't just get the opportunity, they are often outright expected to narrate the consequences of an action resolved by the dice: "how did you dodge that attack," "what did you say that was so persuasive," "ooh, that's a nat-1, how did you insult the King?" etc. And that very last example shows "forced" roleplay as a result of the rules, which I'll address later on.
2. Rule 0, and Rule ... 1?
Sometimes the most positive thing you can be in a boring society is absolutely negative.
Just want to note that I literally have no idea what this quote is trying to say. I assume it's meant to summarize your point but it's completely opaque to me.
The DMG (which no one reads) is chock full of different ways to play- from using dice, to ignoring dice, to ad hoc adjudications. In the end, the DM is the "master of the world" and the "master of the rules" (also from the DMG, which no one reads).
Uh...except they do.
I read the 5e DMG, even though I don't even play 5e very much. Reading the rules, and the advice surrounding the rules, is extremely important for learning how to use a system effectively. Your dogged insistence, here and elsewhere, that absolutely no one reads the DMG does not do your argument any favors.
If Rule 0 is about the DM's authority over the world, then Rule 1 in D&D is about the Players' authority over their characters.
This authority is quite frequently abrogated though, it's far from absolute. I used the example above of, implicitly, a Diplomacy (or maybe Intimidate) check against a king, where the player gets a nat 1--even if not using fumble rules, a nat 1 is
usually a failure for most characters, by the rules. The DM gave an adjudication, one that demands a specific roleplayed response. The player loses their absolute freedom to choose how they roleplay; they must roleplay in a certain way.
For that matter, the idea that the DM authority over the world is probably not that controversial (although I am positive that there most people would articulate that the DM must follow published rules, or must be neutral, or transparent, or communicate, etc. in order to run a successful game).
Yeah, that's definitely where I'm at. There are both rules and principles that bind the DM's behavior. Obviously, just as a rude player can attempt to ignore the DM's adjudications, a rude DM can simply ignore these things. Doing so is ultimately detrimental to the game IMO, but that's a subject for a different thread.
...but this isn't how all TTRPGs operate. There are models that allow Players to narrate results. There are models that allow Players to override the GM's narration. There are models that bind the Players' roleplaying options- just as, in D&D, you lose a combat, in other games you might have to roleplay certain ways as a result of dice rolls or certain events in the game. Which is to say- pointing out the division of authority in D&D, and 5e, might seem banal, but it is worthwhile because it doesn't have to be that way. Moreover, as I go through in the next section, even assuming this traditional division of authority, there is still a lot of play in the joints, and it's worthwhile for those people playing 5e to examine how they play, and how they want to play.
D&D, as you said, permits every one of these things. Players get to narrate their character's backstory, which (at least in most games) usually becomes relevant somewhere along the line, and in the vast majority of cases, if the DM's narration were wildly at odds with what the player wrote or intended, it would be generally expected that the player would
at the very least be given an equal platform for negotiating the final result, if not outright control of the "no, that's not what my backstory said, and you agreed to that backstory" variety.
Looking back at the history of D&D, one thing does seem clear- despite the success of other games in introducing play concepts and rules that affect roleplaying, the history of D&D has shown that (D&D) Players do not like that, and do not want that in their D&D. Whether it's the various OD&D/1e attempts to lore-ifying classes with roleplaying restrictions (such as the proverbial Lawful Stupid Paladin) or ditching the XP rewards and penalties for roleplaying within your alignment, or even the continued movement to ditch alignment- the arc of D&D history has always bent toward complete Player authority over the roleplaying and decision-making regarding their PC.
(Now, I will again say that the DMG does offer some optional rules regarding roleplaying, such as Honor Points, and narrative control, such as Plot Points .... but ... wait for it ....NO ONE READS THE DMG!)
That's a rather big leap there. Players don't tend to like
restrictions on what they're permitted to play, but they quite frequently request mechanics that
support their ability to play specific things. There's also a very common trend of wishing to eliminate, or at least ban/disallow, specific classes that a player perceives as not "fitting" into the "traditional" D&D fiction of pseudo-medieval pseudo-European fantasy. Artificer and Monk are commonly put on the chopping block for this reason. If it were truly universally true that players opposed all restrictions on roleplay, they wouldn't give such roleplaying-centric reasons for opposing the inclusion of these classes.
And, as above, I reject the argument that no one reads the DMG. Plenty read the 5e DMG, and the 4e DMG1 was often celebrated as a hallmark of good principles in running games, even by people who didn't actually like 4e (or even outright
disliked it).
The more interesting question is- what about narrative control? What amount of control does the Player have over the narrative and the environment of the world? I will start by recounting an example I saw where this issue caused a table conflict, and then delve into why this might be important-
Sounds like the problem wasn't "doing something wrong," but rather the neophyte DM and the narrative-heavy player failing to communicate their positions correctly to one another. Newbie-DM expected mostly narratively-passive players, narrative-player expected an active back-and-forth. In the ideal case, these things are ironed out during Session 0, but fresh DMs are unlikely to know that they need to do this. (This is one among several reasons why I so strongly advocate for really,
really good tools for DMs. Old hands like you don't need them, and hence can
get away with totally ignoring the DMG, but newbies can easily get stuck.)
Because D&D has so many rules, and such a concept of the "party" and the "spotlight" and "balance" and "fairness," there can be concerns that unchecked Player Authority over the narrative (the environment) can be unfair or unbalancing.
Now if only we had a parallel concern that the DM, with the incredible power they have to mislead or coerce the party, could create unfair or unbalancing situations through unchecked DM Authority...
One thing I have seen repeatedly is a conflict in that interstitial area- the Player declaration prior to the DM narration. And this is where I think that it is worth exploring, at your own table, what level of narrative control and authorial responsibility should Players have? What is acceptable?
I don't think that there is a single, correct, answer.
In general, there shouldn't be, though I do find that many DMs kinda want to have their cake and eat it too on this front. They want players who are dynamic and engaged and "doing what they want to do," but they also don't actually grant the players much (if any) authority to
do that. IOW, it's less a matter of "there is one right answer" and more "a number of DMs have an answer that contradicts itself."