The closest it's ever come to mattering was when we played a 4th Age Lord of the Rings campaign using Savage Worlds. I had two players who did, at some level, get a bit deeper into understanding what it meant to play a Noldor in the world of Lord of the Rings. They found a deeper level of pathos because they were really exploring what it meant to live as an immortal being in a world that has been shaped largely by the failures of their ancestors, and only partially shaped by the successes. It didn't play out all the time, but there were definite moments where we experienced them playing character traits that meshed with that history.
I want to add to this as a bit of a digression, because.. reasons.
I ran a game of Forgotten Realms where there was some reason for Drow. Subterranean, pitch black, shorter than normal, and matriarchal and a few other things.
So, instead of burying my players in lore to read, or history to read, and not giving them much other than what a "here and now living Drow" would be thinking about. We set out to play.
The game was
nothing but Drow.
You cannot go to the 'surface' - there IS
NO surface.
There are no humans, no dwarves, nothing.
Just you and the endless caves of the Underdark.
Forever.
We took time to play out various cults and factions of the Drow all based around some ancient and vague lore that Corellion, the Sun god had cursed and banished his dark wife, Lolth and her children, to a place
"as hard as heart of stone".
That's the backstory they got,
one sentence.
From this is became easy to roleplay out the disdain women had for men from the reason they were here being because of a 'man'. So our political
matriarchy grew, and it got heated.
Our cults grew as magic was odd, different and without other sentient races, largely not about murder = but
about survival.
Now we see a Purpose for magic, and the specific magics the Drow used/developed/mastered. They needed food, they were desperate for anything more than rare grubs, worms, and fungi. Magic could only aid them so much in this...
Their weapons were for caves, for things with chitin, for digging or climbing or swimming. NO armor, no baggy clothes. Just by playing as an entire race of people trying to live in the Underdark alone, that built a HUGE amount of reasons for why their skin was black, why their skin was tough as iron, why they were short, why they saw in the dark, why their teeth were sharp to crack chitin and tear worn flesh, why they are resistant to mind affects from years of Psilocybin mushrooms...
Evolution and magic drew them to survive!
Their features and magic are now after, derived from, purposeful because of the lore and history of these people.
So...
Imagine then... after a Year of roleplay, after 4 hour games, every week for a year... They broke through to the surface.
I didn't have to aid the players in acting "Drow" around humans. I didn't have to remind them of Drow features when around orcs. They were SO immerse in the personhood of the Drow, that Humans were so alien, farms were so magical, and Golden Elves were demonized after generations of self-mutating drow oral traditional lore and blind faith.
Never had we felt such a truly alien and inhuman "race" in a fantasy game - ever.
And all it took was a few sentences to read. The rest was just the night to night fun of roleplay.
Now, when we later on flip the script, and play as humans or whatever, and these players meet a Drow, they know how strange that interaction is about to be - and it has nothing to do with dark skin or white hair and other frivolous aesthetics
Not to mention the delight and horror new players get when they meet these 'Drow', breaks expectations and enriches their 'otherness' ten fold!
//sorry for the aside. it was just a fun time! and seemed relevant to making races and magic both deeply purposeful.