different races also tend to have rules for how to handle them
So what are the general thoughts on having these in the first place
It's ubiquitous in games, but personally I haven't found it to really add anything beneficial.
Let's say there are elves, dwarves and humans. Elves have +1 dexterity, +1 intelligence, -2 consitution. Dwarves have -2 deterity, +1 strength +1 constitution. Humans have no modifiers.
How does this have any positive affect on the game? It doesn't. Remove it from the game and nothing is lost. All it accomplishes is that min/maxers will choose a race that benefits them, and roleplayers will occassionally be compelled to choose whether to accept numeric penalties to play the character they want.
What about race/class restrictions? That's pretty common too, but how does it add anything to a game? If a roleplayer wants to play an orc mage or troll thief, or whatever...how does it benefit the game to say they can't?
Which brings me to another, more specific question: how do you feel about humans? If you're having racial traits exist, humans present a rather tricky niche, because it's extremely important to avoid pigeonholing them into being representative of any single culture, lest you wind up justly accused of ethnocentrism, but it also typically comes across as boring and uninspired to make humans "good at everything" or otherwise generic.
I'm not sure I understand what the problem is. "Jack of all trades" is the most commonly chosen niche for humans in games. No special benefits; no special penalties. If you're going to have a system that gives gameplay effects based on character identity choices like race...then having a generic default seems pretty reasonable to me. Also, in my experience while a good number of players have aesthetic preferences about race, very few people
object to playing a human. Plenty of people will find it distasteful to be a short, bearded dwarf. Lots of people will find it tasteful to be an effeminate elf. Lots of people will reject being something like a troll or orc. I don't think I've ever had a player say "human? Ewww!" So when you have someone who wants to play, say...a mage....even if statistically it might benefit them to play an elf, if their reaction is "what, seriously? I'm not going to be a tree-hugging pansy" it's convenient to have a race that is functional for any class choice that most everyone will find aesthetically acceptable.
That said, again...the problem can be avoided by not using racial specials.
Note also that I routinely use and have played games with extreme racism as an in-game factor, and I don't recall anyone every getting upset or seriously complain about ethnocentric game mechanics. I think it's a non-issue.
As to culture and pigeonholing...in general it seems to be a non issue. Bad writers and gamemaster might tend to make races members of
planets of hats, but rarely do people seem to have any difficulty thinking of humans as being culturally varied. Sometimes comically so. Apologies if you don't get the reference, but I've read quite a few "human in equestria" fanfics that have identical conversations in which a human spends a paragraph or two explaining to ponies how incredibly varied humans are. That they're so diverse, come in so many different colors, etc. And yet here they are talking to creatures who don't even all have the same number of body parts or means of locomotion.
It's probably an interesting sociological phenomenon if one were to look closely at it...but short version: for some strange reason a lot of people seem to expect humans to be tremendously varied and versatile, while they tend to think of anything non-human as being rigidly defined by a very strict set of criteria. I don't know why. But it routinely pops up in fiction. Again:
planet of hats.
I'm getting a sort of nagging sense that I've pigeonholed
humans into being Western extroverts
Well, cultural trends are a bit different than directly game-play changing mechanics. You're the one making your world. If you make your races such that humans have certain cultural preferences in where and how they live...that can provide useful character to your world. And it doesn't limit characters. If one of your players wants to be an "unusual" human in the sense that they grew up living with a religious hermit in an underground burrow in a desert, no problems are created by this. It only really becomes a problem when you say something like "humans
must come from cities" or "human get special magic abilities that aren't really magic but are just totally arbitrary fluff that goes with being human for no good reason..."
an ability that allows sharing of saving throws*:
...yeah, like that. In what way does giving an arbitrary ability like that to a race have any kind of positive effect on your game?
It's a serious question. Think about it.
Do you want players to look at an ability like that and think "wow, that's useful. Ok, I'll choose to play human because having that ability is more important than having a clearly established persona" ? Do you want players who make choices based on roleplaying preferences to have or not have game-altering mechanical benefits? How does this in any way benefit the game?
My own preference, then, would be for traits that would allow for the trope cultures to arise from the racial traits, without having to kludge your way into it by saying the culture gives a certain bonus. So, for instance, instead of giving a Dwarf a +2 bonus on whatever mining checks you're using, you could instead say that a Dwarf ignores some or all of stone's hardness.
Ok. But if you're going to do that there's no reason to tie these benefits to
roleplay significant factors like race. Instead of giving dwarves a +2 mining bonus, you could give a mining bonus to anyone who would reasonably have one due to character background. If a human character grew up in a mining town, you could give them that bonus. If a dwarf was a member of the merchant class and grew up traveling aboveground selling golden goblets, and they've never picked up a shovel or pickaxe in their life, does it benefit the game to give them that mining bonus anyway just because they're a dwarf? How stupid is it when it turns out that the level 1 dwarven merchant who has never picked up a shovel is just as good or better at mining as the level 1 human miner who grew up with miners in a mining town because his +2 racial bonus is more than the human gets from being a professional miner?
Just ask yourself: do these things we're discussing in any way benefit a game? How?
If you want there to be rules, that's fine. If you want mechanics, that's fine too. If you want complicated systems of numeric penalties and benefits that players can take pleasure poring over to create the most mechanically powerful character...I don't object to that. But I
do recommend divorcing these mechanics from aesthetic factors.
The day you have a player enthusiastically show up to his first gaming session having spent hours the previous night writing up an extensive character background for his female, elven mercenary fighter, complete with separate biographies for his immediately family and has a full page, full color drawing of the character, and a list of personality quirks and tropes and speaks with an accent and uses specific language when speaking in-character...and you tell him that "elves get a -1 to constitution, and females get a -1 to strength. That's a bad choice for a fighter."
...that's the day you realize just how counterproductive it is to connect gameplay mechanics to aesthetic choices.