You embrace the "empty calorie" subclass design / class-as-mechanics-not-identity philosophy. OTOH, I embrace the "recognizable archetype" subclass design / class-as-an-identity philosophy.
The perplexing thing is, D&D does have significant reason to use either (or even both, in a sense).
It makes sense to design a class based on a recognizable archetype(s) from genre, it's a starting point that informs and inspires the design process, and it helps the game to model, or at least evoke the feel of, the genre, as well.
It also makes sense to use a class in a build (especially an MC build), based on what it does, rather than the initial inspiration, if you have a different concept than the genre archetype in question in mind, that happens to share many of the same abilities.
Hmm... I guess that designer perspective vs player perspective.
Either I've been unclear or you've misunderstood. The reason I think the "CORE FOUR" classes all merit more subclasses is because those classes – cleric, fighter, rogue, and wizard – encompass the greatest breadth of concepts.
Maybe if you swap in something more like the genericized 2e 'Priest' for Cleric and Warlock for Wizard - since the neo-Vancian wizard & traditional heal-bot cleric represent a very odd and narrow range of concepts, not even all that evident in the genre.

For that matter, the Rogue is the genericized/rehabilitated(npi), so less narrowly defined, 'Thief' of the classic game.
They are, though, the oldest, most hallowed of D&D classes.
It's absolutely NOT numbers for the sake of blind numerical symmetry.
Symmetry isn't all bad, it can make you think, sometimes. For instance, if they hadn't been recoiling so violently from the Source/Role 'grid-filling' thing, they might have noticed that they'd produced a game that was almost all spellcasters. Or, at least, might have stopped to think about it.
What IS important to me is the radically different priority the designers gave to "many subclasses for clerics & wizards." For example, I could easily imagine a wizard with just 3 subclasses (apologies for the rudimentary names): Blaster, Controller, and Scholar.
Nod. Not traditional, so a non-starter in the context of 5e, but logical.
The Cavalier is inspired by the AD&D class of the same name from Gary's original Unearthed Arcana.
"Knight" just sounds more familiar. Also, the 3.5 & Essentials 'Knight' might've been a good place to look.
The Destined Hero archetype is inspired by young adult literature and is designed to be both simpler and more responsive to player creativity than the other archetypes.
Oooh, sounds like a cool idea.
Definitely going to have to give it another look...
See, I find the distinction between Sorcerer and Wizard really weak because it's mainly mechanistic in nature. Yes, there's interesting flavor writing to the sorcerer but it barely plays out – IOW, the Sorcerer mechanics don't really evoke that flavor of "born of magic, magic in the veins" very well.
It's not that mechanistic in degree, either. At least in 3.x it was a significant mechanical difference, even if they were using the same spells. At least in 4e, they were using completely different spell lists & were of different roles (the Blaster and Controller you posited, above, approximately). In 5e, the Sorcerer gets no unique spells and everyone casts spontaneously, it's tough hanging the whole magic-in-the-blood concept on metamagic.
I understand that players who were really into D&D during the 3e and 4e eras are more comfortable with purely mechanically differentiated classes, and there is a whole group of people who want to shift D&D towards a class-less or class-lite system. But the downside of that it creates a barrier to entry for new gamers.
Wait! The downside is it's unfamiliar to returning D&Ders. New players have no vested interest in the hairs we're splitting which-came-first-the-archetype-or-the-concept. How classes are differentiated is something you find on close analysis. On the surface, they have different names and do different things, they're different.
One of the reasons 5e has done so well with bringing new people to the game

, I think, is that the designers reduced many of those barriers.
I think a significant one is eschewing the rapid publication model that RPGs had used since the 90s, and presenting a stable, if tiny, shelf foot-print. Another major one is attracting and retaining enthusiastic support from the existing fanbase, which translates to experienced players, and especially, experienced DMs, available to teach the game.
But new people don't try the game because of any nuances of how classes are differentiated. They try it because they've heard of it, and, these days, probably quite often, because they were in a game store checking out the current board-game craze....
They could do the same for the fighter's fighting styles, for example, turning "Great Weapon Fighter" into a subclass and attaching additional flavor to it, ... Why I think they didn't do that, as opposed to the spell schools where they did do that, ...because the fighter is based in reality more, or at least something we can relate to more. That's why fighting styles don't make good sub-classes – because they are just expressions of a specialization/technique, rather than an expression of a character.
Another major difference is that choice of Wizard Tradition doesn't close off the spells of the other traditions. Before you apply style, there's not much to choose among weapons (even after you do, there's not a whole lot), but once you have a style, you're kinda locked in. So a style-based sub-class would be very narrow and option-poor, even by traditional fighter standards.
I think that's a great design approach...as a rules option or for a different RPG besides D&D. What you see as a weakness of D&D – the "rigid" classes – is actually one of its strengths
D&D is a classic game, beloved for its flaws at least as much as for its strengths.
Classes /do/ serve a purpose, but that purpose can be served as well, for new players, by sample characters, and more generally, by 'package deals' in a more flexible build system. It just 'wouldn't be D&D' to the established fanbase.
particularly when drawing in new players and facilitating play across games. The classes have history, and provide a recognizable starting point.
History that is meaningless to those new players.
If all the extant D&D fans (and all their books) were just Raptured by a deified Gary Gygax, and WotC put out "D&D" with all the content from RuneQuest or Savage Worlds or whatever between the covers, it'd be exactly as successful at attracting new players. Heck, maybe more successful at retaining those new players, depending on the choice of 'whatever.'
That's actually one thing the PHB is silent on, but was actively discussed during he D&DNext Playtest – what is a subclass supposed to represent? It is a technique? Is it a secret society? Is it a cultural identity?
It seems to be different for each class.