Awhile back I did a kind of mostly mock "review" of 3rd Edition, where I went through the ropes and described its numerous faults in a positive light. To be absolutely clear, I enjoyed playing 3rd Edition quite a bit, otherwise I wouldnt have played it for about eight-fucking-years. This does not mean that it didnt have its faults, which in turn doesnt mean that it wasnt a fun ride while it lasted. We had good times but in light of better games that fulfill the same genre, its not nearly as fun.
Really, my problem with 3rd Edition wasnt even necessarily the fact that the rules didnt support the genre but the rules themselves. In fact with the exception of some clunky subsystems like Craft and Profession, I think more or less did a pretty good job. All editions were action-adventure fantasy role-playing games at heart. Fantasy because they have magic and supernatural creatures as major elements, action games since they emphasize lots of physical challenges, but also adventure games because they contain puzzles and challenges that are not necessarily solved by brute force.
In my review, d7 made a comment that action-adventure is only one of many genres that Dungeons & Dragons inherently caters to, citing dark fantasy, exploration, and "sweeping politcal epics" as examples, all of which I disagree with. I dont think of either dark fantasy or exploration as true genres, but more like themes or styles, and I dont think that editions before 4th support political games very well at all because of how skills (if they even existed) worked.
Dark fantasy is really just fantasy with some horror typically added to the mix (most often high fantasy or swords and sorcery). We saw a lot of this in Elric and stuff by H.P. Lovecraft, and its really easy to do to the point where DMs might do it and not even realize it. Its very popular to the point where there is plenty of advice online on how to make your game scary, as well as more official support.
As for exploration? I'm not sure what the criteria is to categorize a game as "exploration," but that seems like it would inherently be a part of many games by definition, as often the party is touring around in some forgotten or unknown location, so...yeah. Its not listed under any genre, whether you check literature, film, or game.
A political game is one such theme that I dont think worked well at all before given the mechanics, but can be pulled off a lot more readily in 4th Edition thanks to skill challenges and the way skills function. It is because of this that more people can get involved with this process than they ever could before and provide actual assistance if not success, and with XP rewards built into the mechanics players can improve their characters without ever making an attack roll. You probably wont use many, if any powers (except for utilities), but if you absolutely must use this game in this fashion it would work out well enough.
The best games are those that pick a focus and work on emphasizing that. They dont try to spread themselves too thin or entertain everyone regardless of the games they like. A lot of people enjoyed God of War, but disliked the few spots where you had to pause the action and have Kratos manipulate what amounted to a tetris-puzzle in order to proceed. It made for a rather unsatisfying anti-climax, where Kratos rips the heads off a bunch of minotaurs, and then starts to reassemble wall-space in a slow and precise manner (this is why in the sequel they removed a lot of the ones that ground the game to a halt).
Note: This not to say that I'm opposed to intellectual puzzles, I just dont want them in a game where it seems shoehorned in.
So, yeah. In a nutshell: D&D is an action-adventure fantasy game. Always has, and likely always will be. Action-adventure games are incredibly popular, so it makes sense, but note that action and adventure often go hand-in-hand and are very open to including other genre elements. I think that D&D as written can shift perspectives to easily cater to either extreme, but the rules didnt lend themselves well to other genres that fall outside of the scope. This isnt a flaw, mind you. There are other fantasy games that cater to other genres and styles. My opinions in my review still stand, given that it wasnt even really about the genre. I mentioned it at the start, but the game falls flat because of mechanics and execution.