That said, a lot of games of D&D just don't care for PC's society roles at all. Originally D&D is a game about adventures, and that's how the classes were always designed. An "Elf" class is a perfectly valid concept, when the game is only about adventurers, and that "Elf" is simply a short name for "Elven adventurer class". It doesn't mean all elves belong to the Elf class, just that all elves adventurers do. And if the fantasy world being used in this game has Elves living secluded in their mysterious cities, Dwarves living closed in their mountains, and Halflings rarely leaving their shires, it makes a lot of sense that the few who are seen in the adventures are adventurers.
Note that this is not necessarily what I prefer personally... I'm just saying that the assumption that all demihuman races need to have fully-defined societies similar to humans, is not the only way. And it actually might even work against the otherwise very good purpose (IMO) of trying to make races more interesting by being different.
Okay, look. Here is why that sentiment is crap.
First, consider that you are talking about an entire SPECIES. At least a full NATION of people. Independently existing, capable of surviving on their own.
Well, to begin with-- if the society has ever advanced beyond the most basic of tribes, then you are going to inevitable have class stratification. Even if your people are the most extreme communists in the book, assuming the race has a steady supply of food, lumber, rock, metal, leather and so forth-- which they MUST in order to have been able to survive in this world, we can easily surmise that the race has farmers, woodcutters, quarry workers, miners, shepards/herders, smiths, and leatherworkers.
Does the race have a home? Great! Then you have architects and construction workers. Do they dress like cavemen? If not, they have designers, tailors, jewelers....
You get the idea here. Point is we are talking about a whole gamut of labor going from the unskilled labor that requires virtually no education to requiring a fair bit of education. And this group of people are going to have a culture of their own differing from job to job.
Now, on top of this you are going to have those people whose purpose in the society is not going to involve much work at all. It'll be all about decision-making and delegation. And they will have thus more free time to pursue educational and recreational goals. The ruling class, the clergy, the aristocracy... they are going to differ extraordinarily from the lower classes. They are not going to have the same values and ideals, habits or personality. It is just simply impossible. And this is why portrayal of demihuman races tends to suck-- the ignorance of the simple fact that you aren't going to have a living species that universally has the same personality and same abilities.
Finally, you are going to have a counter-culture. This is inevitable because a people's idealized images of themselves are never going to match the reality. Whenever the overall culture swings too far in a direction, a counter-culture is going to spring up to push in the other direction. If the society is racist, the counter culture will be anti-racist. If the society is religious, the counter culture will be anti-religious. If the society is materialistic, the counter-culture will be anti-materialistic. And all of this can work in reverse too. Generally it doesn't work along the axis of good vs. evil, although you'll hardly ever convince people on extreme sides of the divide of this, it is more of a Law vs. Chaos thing. Counterculture members generally come from the middle class and upper-lower class, members who generally feel that they are being judged unfairly by the current values of the society and then people in the lower class follow them.
So once one starts to get their head around the nebulous thing that a society really is and how it is layered, one can begin to understand the folly of how the portrayal of races as clones rolled off an assembly line really is. Of course, little of this has to do with class roles, but it does have a lot to do with backgrounds and fundamental assumptions that all members of a race will have exactly the same skills and abilities.
Next, you have to consider what a society needs in terms of class roles.
First, the easy one. Does the society have a standing army? Has the army ever been capable of winning a war? If so, then guess what? You have to have Fighters, Barbarians or Rangers of some sort. Of course, this is the easy one. When OD&D used demihuman classes, it was attempting to create the race's version of a basic soldier.
Of course, Ranger societies exist outside of racial and national boundaries. Those who leave their society and become Rangers do not need to be of a part any particular race. They are dedicated to the protection of the forest and pretty much welcoming to anyone. Of course, there are some societies that naturally have hunters and scouts that would naturally utilize the same skills and abilities as Rangers do, those that live close to the wild and rely mostly on hunting-- Elves, Goblins, Orcs, Gnolls.... races like these would have Rangers. Maybe in exclusion to Fighters, but not definitely so.
Next, does the race have gods? Do the gods actually assist them? If not, your race has already been wiped out of existence. There is no possibility they could have survived the threats of their world or stood up against enemies who have priests if they have none. If so, then one could well presume, as all editions of D&D did, that the gods are more prone to answering the prayers of those who have shown them extreme dedication and that there is an organizations or at least individuals totally devoted to the divinity. Guess what? This means you DO have Clerics! Cleric MUST be an option for your race. Now, I suppose more feral and wild races might exclusively have "Shamans" or "Witch Doctors" (i.e. Druids instead of Clerics), but at the base you have a separate class of people here.
Oh, and if the race's god ever has battle-hardened champions that enforce their will (and what god doesn't?) then they have some sort of order of "Paladins" whether or not they use the name "Paladin".
Next, let's consider the Rogue class. The Rogue class can represent many things. First, there are thieves or other criminals among your race. If there aren't, you haven't created a race-- you have created a group of 2-dimensional strawmen. Every nation, every people are going to have thieves or assassins or similar sorts, it is inevitable. Rogues also can be dedicated scouts or spies for the race's military, they can be scholars or diplomats, they can be skilled craftsmen or mechanic. In short, Rogues are a catchall class that represent so many aspects that every single race needs to have that it is impossible to have a race with any sort of civilization or culture who does not have some sort of Rogue.
Finally, Wizard. You know-- the whole presupposition as to why technology in D&D worlds fails to ever advance is because magic does everything that technology would do. Thing is... if a whole people don't have any access to this power and yet are supposed to have build large cities... are supposed to militarily keep up with their rivals and enemies who do have it? They'd be gone. There is just no way they could manage it. Every race is going to have some one dedicated to studying the arcane arts. Although they might not have the exact trappings of the Wizard, they would be mechanically close enough to count. You might just explain the way they go about creating their effects (i.e. instead of memorizing spells, they craft runes and when they use the spell the power of the rune is expelled.)
Now, there are other classes that can just spring up even if it isn't the primary focus of a people.
Bard-- there is nothing biologically that would prevent any race from learning Bardic arts from any other race. Although Bard is a far too narrowly defined class for its key abilities since, yes, I can imagine not every race having a giant focus on music... but, it is still something that all could accomplish.
Sorcerer, Warlock - Yeah, these have very little to do with the race itself and more how an individual has been affected by supernatural forces. This means there are very, very few peoples who could be said to never develop these abilities.
Do you begin to understand the picture yet? You cannot put out one class and say "This represents absolutely everything every single elf in existence is capable of doing" or even "This represents absolutely everything any elf who chooses to adventure is capable of learning" because among a single people there are going to be divisions and specialties.
The only way it makes sense, the ONLY way-- is if there is no such thing as a race at all. If elves never, ever, EVER exist as their own culture or nation-- EVER. They never have and they never, ever will. The only time Elves have ever existed is when they had the other races on hand to fill every single aspect of their society needed for societal survival from the very first time there was such a thing as an "elf"-- and even then, EVEN THEN, to posit that it is biologically impossible for them to learn other classes is madness. It in the very least presumes that every single Elf in all of existence has precisely the same personality, same background, same interests, same societal role, same inclinations and same drives and motivations and ambitions.... And that is not a RACE. That is a CHARACTER. That is one very specific character.
So, one last time-- the whole idea of racial classes is stupid. The idea of hardline racial class limitations is stupid. Even the idea of a racial starting classes is stupid. Because none of it, NONE of it, makes any god damn sense if your game has a depth beyond an 8-bit dungeon crawling action video game or a maturity or comprehension level above that of elementary school literature and history class.
You couldn't even create a class and try to say "Well, here is your standard elf" because what the flip would that even be? The guy dedicated to the Elvish God who channels his goodness and blessings onto the world as "standard" as the Elven mystical scholar in his ivory tower keeping the most ancient secrets of the world who is just as "standard" as the master huntsmen who protects the Elven enclave who is just as "standard" as the penniless Elven trickster who uses his stealth and sleight-of-hand to play tricks and cons on his fellow Elves who is just as "standard" as the one who taps into her ancient fay heritage to channel brilliant magical powers who is just as "standard" as the Elf who is at one with nature and befriends the animals and can become one with them who is just as "standard" as the golden-armored champion of her people armed with a spear and shield and ready to defend the enclave against all who tresspass there...
Every single one is just as much "standard" as any other one. Every single one through a series of unfortunate events could end up separated from his people and end up rounded up in a group of adventurers. So there IS no such thing as a standard Elven adventurer-- because not only can you not craft a class that represents every single possible member of the society, not every single member of the society has all the skills and abilities of every single other member of the society. And it doesn't have to match whatever the hell you think "human" society looks like either. It just merely needs to have division of labor and specialization, two hallmarks without which you do not have civilization.
You know, maybe that is part of the reason idiots keep insisting Elves need so many endless subraces that are statistically ideal for every class in the book. It is because other idiots keep insisting that Elves can only have one class and only one class and must perfectly match one single Character exactly without the slightest of deviations and then an idea pops into their head that seems "elvish" but doesn't 100% match that one exact character the other idiots seem to be willing to call an "elf" and so they think a whole separate subrace is in order... when in fact, all these different "subraces" probably just represent different members of the same exact society.