Whatever the DM or world creator wants. Players use them just fine. So does Eberron. So does Dark Sun. There are multiple factions of them in the Nentir Vale. I've stated what they do in Warhammer. That the Forgettable Realms don't use them is a reflection of why I've always found it a tedious setting. That said I prefer Realms halflings to Dragonlance ones.
None of that answers the question.
I started this off saying that we needed to talk about narrative role for the halflings, and that if you removed them from most settings it wouldn't affect the setting at all, and that most people wouldn't notice.
You immediately declared that that was not the narrative role of halflings. Definitively and went on to tell me that there are 4 to 5 players for every DM.... completely skipping out on the fact that you never stated their narrative role. Even as you tell me that setting writers and adventure writers are simply too lazy to use them correctly.
Now, when directly asked the answer is... whatever you want. But their narrative role isn't "whatever you want" because if it was then they'd have even less of an identity than they do. Also, while Dark Sun has a unique take on them... they actually don't affect the setting in a meaningful way as the players play. They live far off in the corner of the map, where the land is completely different and are cannibals. It is only if you dig into the origins of the planet that you might learn more about them, and if you do... it still doesn't matter. It is like reading a fantasy novel set in a fantasy world with fantasy characters and at the very end they reveal that you were America circa 8,000 CE and that the modern world fell so long ago that no one remembers. It doesn't really change the story in any way, the story was the exact same without that "twist"
So, do you actually have an answer for what narrative role halflings play, or are you simply going to go with "I can make up anything" to somehow prove me wrong that... what, they have a narrative role? I mean, I never stated one in my original post (which mentions Eberron and Darksun) you just declared that I was wrong about what it is.
Nah. It points to the way they were used in Dragonlance. Tinker Gnomes, Gully Dwarfs, and Kender are all bad comedy races.
And what does that have to do with the lack of tools being a defining character trait in 5e? I mean, great I guess, you can't get past gnomes as they were presented in Dragonlance, but I'm somehow terrible for looking at how halflings are used generally and not across every setting ever published in any medium.
Also, by this point in your reply, you have literally skipped half my post. This is 12 paragraphs in. I addressed your ridiculous claim that forest gnomes are knock-off lightfoot halflings. I addressed your view that forest and rock gnomes are somehow opposing forces. I covered why forest gnomes are amazing in the forest. I covered Rock Gnomes should get more than tinker tools.
Are you simply agreeing with me and moving on?
And if I didn't know D&D the picture below is a gnome. And "half of a thing" is half the size of a [human] thing. Which tells you more than "gnome" does.
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And? Quite literally that statue could depict a halfling. They are a small person after all.
Tell a random person on the street about "gnomes" or "goblins" or "fairies" and they likely can at least get a context for what you are talking about. Ask them about halflings and they might ask you if that is a new sale down at the diner.
Just because garden gnomes exist doesn't mean gnomes don't have an identity. Googling "Goblin" gives you a lot of different images, some of which you wouldn't even think were goblins if they weren't being pulled up as results.
You've two different concepts tangled there that about half of modern urban fantasy mythology tries to disentangle. A Fairy is a small winged magical creature and the Harry Potter ones draw from the same well as Tinkerbell. The Faeries, the Fair Folk are a different kettle of fish.
I'm not tangled up at all. That's my point.
Tinker Bell is far more likely to be what people in the mainstream culture talk about instead of the The Fair Folk. Yet, the Faeries aren't made meaningless and garbled because of the Fairies. So, why would gnomes be meaningless and garbled because people buy garden gnome statuary?
Are dragon's meaningless because Chinese Dragons are very different from Western Dragons? And even Western Dragons vary widely? No. So, we should apply the same standards evenly.
And the 5e D&D version of gnomes is possibly the least interesting possible version (except possibly the dwarf wannabes from AD&D). It's a halfling putting on airs. At least the 4e ones had a connection to the feywild and were thus meaningfully part of the Fair Folk. There is plenty of room for something that't actually different and more mythical - but that's not the 5e one.
The original gnomes, as introduced by Paracellus were earth spirits (even rock gnomes fail at this), 18" tall and that could move through earth. And having halflings there should free gnomes up to be at least as magical as genasi. But instead we get gnomes that are halfling wannabes.
I went into great detail about how they are not halfling wannabe's in my previous post. Gnomes in 5e are also tied to the Fey, I don't know why you think they aren't, except maybe missing the Fey Ancestry? But Gnome Cunning does the exact same job in a lot of ways.
The only thing I can imagine is that you are conflating anything short with halflings. Which is silly, but since you seemingly ignored every single thing I said in my last post to pull out the least relevant bits to try and knockdown... I can't really do more than guess at how you can possibly think that gnomes are somehow lesser halflings. They have a much deeper place in the worlds of DnD, and are far more interesting than the halfling.