True enough.
Though D&D has never or rarely claimed to be a generic or universal RPG. It has attempted to cover a wide variety of settings, but a certain amount of setting expectation has often been baked into it, and explicitly so, from the start. Vance-style magic, for example. Clerics not being able to wield pointed or edged weapons. Demi-humans having class limitations and level limits (which Gary talked about in the first DMG, and Zeb did in the 2E one as being to ensure the primacy of humans in most settings), the existence of Aragorn-clone Rangers who get damage bonuses against certain monsters...
WotC-era D&D removed some of those elements (like race limitations on class and level), and made the game more generic in terms of what kinds of fantasy settings it can accomodate, but not all of them.
That's an interesting idea. Like B/X but with more classes. Humans get the Core Four (plus maybe Monk? How about Barbarian or Paladin?), demi-humans get the rest. In 5E this would be tricky, though, because 12 classes but 10 species.
Cleric: Human
Fighter: Human
Rogue: Human
Wizard: Human
Barbarian: Goliath, Orc
Bard: Halfling, Gnome
Druid: Aasimar, Elf,
Monk: Goliath, Gnome
Paladin: Aasimar, Dragonborn, Dwarf, Tiefling
Ranger: Halfling, Elf
Sorcerer: Dragonborn, Dwarf
Warlock: Tiefling, Orc
I think most folks want more options than this, but it's a fun notion to play around with.