D&D has good bones, and is only moderately difficult to hack well. It's a big tent with lots under it. But the rules provide mechanical support for certain types of play, and other systems can provide mechanical support for types of play other than D&D, while not providing a D&D-feel. D&D does cover a wide spectrum, but other games cover other parts of the spectrum, wide or small. It's only by understanding and using a wide variety of different games with different goals that one can truly cover the whole spectrum.
So., this isn't exactly what I was getting at, and it's kind of a separate post. But here's the gist of why I don't agree (building on the last paragraph of the OP)-
Yes, some games are INFINITELY better at certain things than D&D. It's not even close. Heck, trying to get a
Fiasco-like experience out of D&D? Yeah, good luck. Or, for that matter,
BiTD- sure, you can do a heist in D&D, or advance in a criminal organization, but it's not exactly made for it.
In a way, its similar to kitchen gadgets (the good ones). There are a lot of great kitchen gadgets that are perfect for certain things- a cookie scoop, if you're into making lots of cookies. A rice cooker. A lemon juicer. Heck, maybe you need that Williams-Sonoma stainless-steel pineapple slicer and dicer because you make so much pineapple pizza. I am not saying this to be a dismissive Alton Brown, by the way- things that are purpose-designed for a task will be better at it.
It's like that with games- there are a lot of great games out there that superbly cover a narrow niche- either a narrow genre niche, or a narrow gameplay niche, or (usually) both. If someone said, "I have a group of really enthusiastic gamers that wants to play a cinematic-style heist game," I probably wouldn't be recommending D&D.
But that's not what I'm getting at. Your concentration on what
the rules support misses what is popular about D&D. This is where I draw the line at the people that are hard supporter of, um ... let's say
rules matter. Because D&D isn't just about what the rules support ....
1. It's about what the rules
don't support. The negative space in D&D (the places the rules don't exist) is actually an important feature, not a bug, of the game.
2. It's about the community of D&D. Right now, I can play a game of D&D with a grognard who is running a highly hacked version of OD&D with a 200-page player supplement that, inter alia, details how he allows the
original White Dwarf Barbarian as a playable class, or I could play D&D with a group of high-schoolers that use a lot of 5e homebrew to make it an anime/manga game with Wuxia influences. And all of those people are communicating and cross-pollinating in the greater D&D community- something that no other game has, and no other game is even close to having (in terms of both size and history).
3. It's about the flexibility within the game- this is, perhaps, the most important. Building on what
@Gradine posted (re: types of fun), D&D has a long history of being able to engage different kinds of players, seeking different kinds of fun,
at the same time. On these boards, we often hear about groups that try another game for a while, and then "return to D&D." I suspect that this is because a lot of games are built to
primarily appeal to certain kinds of fun, but are not as engaging for all types of players. Take
BiTD, for example- it's a great and brilliant game. But players that are really into narrative, discovery, or abnegation (yeah, I don't like submission either) ... maybe not so much?
And that's where D&D (esp. 5e) can shine. Yes, the drawback of it, the failure point, can be a bad DM. But a good DM is able to run session so that players who enjoy different kinds of fun can get their needs at least partially met during the game. Just run through the categories-
a. Sensory Pleasure- I like to roll dice and move miniatures and paint miniatures and look at the maps.
b. Fantasy- "Olaf's honor demands that I kill the brigand!"
c. Narrative- Well, that's what the APs are for, right?

d. Challenge- "+2, +1, or +1, +1, +1? THIS DECISION WILL HAUNT ME FOR THE REST OF THIS CAMPAIGN!"
e. Fellowship- Yo, who ordered the pizza? No evil PCs, right?
f. Discovery- I like to draw the maps, and take the notes, and write down the treasure. Wait, there's a rumor of a lost town?
g. Expression- Just wait until you read my 58 page character backstory!
h. Abnegation- I'm here to drink beer, eat pretzels, and play a champion. Now get out of my way and let me roll that d20.
D&D is not a
great game system for everything, or every person. But it's a
really good system for a lot of people when you have groups with mixed interests. IMO, etc.