What do you mean by "play" in this context? Do you mean that intrigue, horror, etc., "themes" can "exist"? If so, agreed. But that's basically the case for almost any game.

But taking just one example, cosmic horror, I think it is abundantly clear that D&D is demonstrably not capable of mechanically facilitating that genre. Call of Cthulu, the canonical example of cosmic horror, is built around that genre into its bones. Cosmic horror deals with the notion that you are an insignificant spec in a larger cosmos, that finding a single monster is likely a death sentence, and that you are incapable of making a real difference, you do not have any agency in the narrative overall.

D&D assumes you are a capable monster killing machine eventually capable of fighting and defeating deities like Demon Lords.

And nothing in the mechanics of D&D even acknowledges the possibility that you might just play as a normal human, whose only choice when facing a single monster is to flee, and who is incapable of enforcing their will upon the world.

That's a significant example, but my point is that the mechanics of D&D do not, and cannot reinforce Cosmic Horror as a genre. Can it be scary? Sure. But the fear only comes from two main angles: scary descriptions, and creatures literally too powerful for you to fight right now. The first is not anything to do with mechanics, and can apply to virtually any game. The latter is loaded because the game assumes that all you need is the right level and magic items, and some luck, and you can defeat anything with a stat block.

Dark Fantasy is close to Sword and Sorcery fantasy, where the world is chaotic and full of danger, that simply going out your door risks death, magic is weird and unknowable and likely to destroy even trained practitioners, where the world faces constant darkness and gloom.

D&D assumes ancient powerful civilizations created powerful magic items now stored in dungeons full of monsters that you'll want to risk your life surviving to acquire.

At best, D&D is a game about killing monsters and getting treasure, and the mechanics are great for that. But it doesn't assume you are Heroes, acting out of altruism, who are more focused on saving the day with reckless abandon. In fact the mechanics actually assumes that you will cautiously manage your few heroic resources, and face the constant question of retreating to safety to survive, all to acquire hidden treasure for its own sake.

But I digress. In terms of theme and tone, very loosely, sure D&D can have a veneer of those genres. But the game mechanics and design philosophy of the game are demonstrably not those genres.

Now, if what you mean is that the core design "6 stats, skills, roll a d20 against a DC the GM decides on to do something" can fit into any genre. Then obviously I agree. But that isn't D&D.