@Imaro, on the general matter of "Does D&D have X
to support game genre/style Y?" I would say that there are a handful of ways that a game can offer genre support. If I'm saying that another game is better equipped for supporting something than D&D, then I am probably not necessarily referring to strictly one thing, but likely one or more of these things. We can even talk about this without discussing so many people's current darling game of BitD.
(1) Mechanical Tools: D&D 5E does have a flexible and ever-growing mechanical toolkit, but I think that it is an
intentionally rudimentary one. It has a minimal skill list, for example, but those skills are broad, vaguely defined, and left incredibly open-ended and reliant on GM discretion and "rulings not rules" particularly when a roll is called for, the difficulty, the Ability used, and refereeing rules/rulings. What doesn't fall under skills will typically require a general Ability check.
Most games will have at least rudimentary tools to cover gameplay basics. Some mechanical tools exist as add-ons. Some tools will require using supplement books. But some games will have more tools. Some will have more genre-customized tools. Some will have more flexible and generalized tools.
Additionally, whether the GM can make their own tools to do X ventures towards the Oberoni fallacy. But it's also a banal point that is true for any given system. But the amount of work required to do so will vary between systems and GMs. What works as a "good enough" solution for one GM will not work for another.
We can say that D&D 5E has some tools for running Arthurian Romance (e.g., "Can I haz midevil kombat?"), but clearly Prince Valiant and Pendragon will both have greater mechanical tools for supporting trope play. That's even true for combat. Let's take a staple of Arthurian Romance: e.g., jousting and mounted combat.
I have played D&D for 20 years, and I know that other people have been playing longer. But in all that time, I can in full honesty count the number of times mounted combat has come up on one hand with fingers to spare. I recall conversations here and elsewhere about the Paladin in 3e, where people treated the free horse as a negative because horses hinder dungeon crawls and feats specializing in mounted combat were trap options. I know rules for mounted combat exist in 5e (cf. PHB 198), but I have neither seen them used or referenced nor anyone take the Mounted Combatant feat in 5e. Nor have I seen anyone take the Cavalier Fighter subclass. Mounted combat provides no combat advantages apart from speed unless you get the Mounted Combatant feat. Which skill do you use for mounted combat by the way? Doesn't say here under "Controlling a Mount." Presumably Animal Handling when conducting risky maneuvers.
Compare that with Pendragon (5th ed.) where it tells me flat out, "Horses are essential to characters in Pendragon, for they give many advantages in combat" (p. 121), and, indeed, we are told that your character starts with FOUR HORSES! as part of character generation. And this game talks plenty about Jousts and rules for Tournaments. Included in skills are Horsemanship, Lances, and Tourney. Even the Recognize skill suggests that I can use the skill to piece together a face with a jousting style. Mounted combat confers more than just "cool, you're on a horse now" as an advantage in combat. Your added speed and height advantage sitting on a horse translates into actual combat advantages.
(2) Play Procedures: The play procedures hopefully meaningfully interact with the mechanical tools for guiding the shape of play as well as helping to cultivate the genre experience. Do the feedback loops and game procedures of play reinforce the tropes and genre? The game procedures, for example, of Agon will constantly reinforce that you are Greek heroes who seek to bring glory to your name. How? The game's play procedures will have you speak your name, apply your epithet, invoking divine favor, and reciting your deeds as part of contests. The play procedures support the ancient Hellenistic heroic tradition. Obviously you can use D&D to broadly play in the genre of Hellenistic heroes: see Theros. (You're still playing Wizards, Paladins, Druids, and such in Theros though, which admittedly tend to fall outside of trope play.) But in terms of play procedures, one game supports that aspect of trope play more than the other. Would I use D&D then for more detailed grueling combat? Honestly? Probably not. I would be more tempted by Runequest, Mythras, or Jackals (Osprey Publishing), which all use the BRP system.
Additionally, on the GM side of things, this may also include random tables for generating thematically appropriate content: e.g., wandering monsters, traps, treasure, rooms, etc. In the case of the Leverage RPG, I can consult tables for generating a capers situation: i.e., client, problem, pressure, mark, mark's angle, mark's power, mark's weakness, mark's vulnerability, who else is in play, the twist, etc. There are also rules for applying Flashbacks. Stars/Worlds Without Number provides a lot of procedural tools for running sandbox games.
(3) Genre/Play Advice: Apart from mechanical tools and play procedures, there is also active support in the form of just genre advice or how to use game X to run genre Z and/or game mode Y. Let's say that I want to run a dungeon crawl, a caper, or a horror story. How do I that? According to some unhelpful advice in this thread, I simply "git gud" as a GM. But what I would hope is that either a core rulebook or GM/Keeper's guide would provide me with some basic how-to support and guidance so I don't have to go fishing for advice online. Can I run mysteries or investigations with this game? Obviously so. Can I do so without needing to consult the Alexandrian's three clue advice for actively running them? Maybe. Some advice will be more thorough and developed than others.
Does D&D 5e DMG have advice for running dungeon crawls? Sure. But I don't think that the advice there is all that great. Basic D&D (whether Holmes, Moldvay/Cook, or Mentzer) and/or OSE IMO provide better, more developed, and useful advice on running dungeon crawls because that's what their games are primarily about. The Leverage RPG provides a tremendous wealth of GM advice for the heist/capers genre and how to run them: understanding jobs, the client, the mark, supporting characters, briefings, challenges, flashbacks, twists, typical heist settings, framing scenes, etc. The upcoming Ravenloft will likewise undoubtedly provide advice for horror play, though it will also be advice with D&D's gameplay and brand of fantasy in mind.
On the whole, I don't think that 5e D&D
excels in providing solid genre advice style support. It has it (e.g., Ravenloft with running horror), but I don't think that the writing in this regard has been a strong point this edition. But a recipe that says "Here's most of the ingredients. Here's a picture of the dish. Figure it out yourself!" will obviously not be as useful as one that provides advice on the step-by-step cooking process, things to watch out for, typical problem spots, etc.
(4) Centrality to Prototypical Gameplay: This dovetails with the above points. While I think that add-on options are available to D&D, such as in the DMG or supplements, which can assist in genre emulation, I think that we can agree that add-ons are generally not part of core gameplay. Furthermore, D&D 5E IMHO is NOT a generic toolkit system like the Cypher System, Fate, Cortex Prime, GURPS, etc. It's not a generic fantasy toolkit system either. It's D&D, which is great and fine if you want to play D&D. It is its own own brand of fantasy, much like Call of Cthulhu is its own brand of horror game. D&D can do other things, but it's either being layered on top of D&D or moving D&D away from what we might call its prototypical gameplay.
@AbdulAlhazred has talked about this a lot in this thread where it's clear what the prototypical gameplay for B/X looks like: i.e., skilled play dungeon crawling. And the mechanical tools, game procedures, and genre advice are all meant to support that prototypical gameplay experience. B/X obviously can do other things, but doing so moves it away from the core experience. Stars Without Number can be used to run neo-traditional games that are about GM cultivated stories, but doing so moves it away from being a game designed to support running OSR-inspired sandboxes.
D&D 5E is not designed to do horror, for example, as part of its core prototypical gameplay. It's prototypical gameplay is neo-traditional style (super)heroic fantasy adventure with sub-classes that have been inspired by popular anime, superheroes, and even Star Wars. The DMG provides some options for changing this up to do horror as does the Ravenloft book. But the prototypical core of 5e gameplay is going to be about that (super)heroic fantasy adventure. I do think that system matters in that regard even within the sphere of D&D but between editions. I'm sure that you recall that
@Bedrockgames has repeatedly reported how different and off-putting Ravenloft was in the context of 3e D&D as compared to his initial Ravenloft experiences in either 1e or 2e. And one can only imagine how he would have reacted to Ravenloft were it adapted for 4e. Part of that involves the expected prototypical gameplay experience for 5e in comparison with other editions.
So maybe it would help, Imaro, if you could provide your sense for how D&D 5e rates on a scale of 1 (low) to 5 (high) on how D&D fares with Crime Capers (for example) in comparison with other games using this sample criteria: e.g., Mechanical Tools, Play Procedures, Advice, and Prototypical Gameplay. If I'm missing something as well, I'm open to that. But maybe it would help to provide some rudimentary multi-faceted metrics for how well you think D&D supports X.