This is something I don't get. It just doesn't compute, perhaps because I never got a chance to actually play DnD until 4e (DM ran Darksun) so most of those races seem standard DnD to me.
Assumptions absolutely are based on one's edition of introduction. So yes, starting with 4e is a huge influence on how one will see commonality and availability of races, level and prevalence of magic, etc.
The two breakpoints I'm familiar with are 2e or early 3e to later 3e, and 3e to 4e. People who played late 3e with a lot of the supplements might not have experienced the breakpoint from 3e to 4e.
There may be an earlier breakpoint from OD&D to AD&D, but I wasn't gaming back there so I can't speak to it.
So, just for the sake of discussion, for folks who would not allow certain races in their campaign....let's just say that you had to allow it. You're running Dark Sun, and there are no gnomes in Dark Sun because they were literally wiped out centuries before by one of the Dragon-Kings. It's a built in fact of the setting.
A player comes to you and says I want to play a gnome. How do you handle it if you can't simply say no? What would you do?
I really like 5e gnomes. Especially the forest gnomes.
That said, I would hate to allow a gnome in Dark Sun, because I like the world with the standard toppings and I don't want to add anchovies on it.
That said, if we are doing a thought experiment, I'd bring the gnome in from another plane (or crash on a Spelljamming ship). The reason I can do that is because all of my D&D campaigns are theoretically set in the multiverse that includes all of the other official settings that were around at my point of timeline alignment. (That means no 4e points of light setting, and I'd have to have a copy of the 3e Eberron book to approve it.)
See, but, here's the rub - why does that have to be 100% on the players? Why is it the players have to learn to accept "no"? Isn't there some point where the DM should put aside his ego and let the player have what the player wants? It's all very well and good to talk about "respect for the DM", but, that's a two way street. Again, presuming everyone is acting in good faith, the player isn't trying to "pull a fast one" when he asks to play a gnome in the game. The player has a concept that the player feels fits with the campaign.
This is a huge point that I don't think has been brought up yet. There is a big difference in practice between a player that doesn't care about where or how his character fits your campaign, and just wants you to make sure he can play it, and a player who has an understanding of your campaign and thinks that once you understand his character you will see that it is a good fit.
I have no problem with the second type of player. As strict as I am, I find myself to be rather a pushover to a well-reasoned request. Take my questing knights theme adventure where the options were explicitly given (each player must pick a different one): Fighter (Champion or Battle Master), Paladin (Oath of Devotion), Cleric (War Domain), Bard (College of Valor). One of my players (who had several options if I didn't approve his first one), pitched the idea of a Ranger (Hunter) with Magic Initiate (Druid), as a knight warden in his land who was secretly a follower of the out of favor druidic traditions. And, in fact, he
asked me if there was a druidic tradition. It fit in my world perfectly, and while I would have liked to have seen the Lore Bard (I had a reason for those specific classes), it was too reasonable and fun for me not to approve it. When I received questions about why some other subclasses weren't allowed, I explained exactly why the limitations were in place (Divine Domains were tightly integrated with specific churches, Oath of Vengeance paladins are a specific order). Everyone seemed perfectly okay with the limitations once understood. It seems to me that the only conflict that reasonably would exist here would simply be coming to understand one another. With this type of player, once understanding is reached, it seems that agreement should follow.
The only place the first type of player has at my table is if I ran an adventure that explicitly was "wide-open 5e". In Lost Mines of Phandelver (and a follow-up brief adventure at high level), I told the players that we were more or less going by the book (a few minor house rules), and if they wanted to play any of the stuff I wasn't going to allow normally to do it now. We ended up with a Dragonborn, a Tiefling, and a Drow, and 3 humans. It was a fun campaign, but not how I normally run it. In my normal games they play in a multiverse where none of the 4e materials happened or will happen (everything beyond 1371 DR (for the Realms) is the undetermined future).
A world-building informed strictness isn't about gaming openness on the part of the DM
as a person. If my players begged me to run a D&D adventure (I'd go 10-12 sessions, but I'd draw the line at a long campaign) based on the 4e default setting (or even with the 4e rules) because they really wanted to do something that required it, I'd be likely to do it (once), and I'd make it fun for everyone if I could. But I'd consider it doing something different, just like if I were playing Savage Worlds or Fate or some other non-D&D game.
When I'm running my normal D&D adventures or campaigns, ie, when I'm DMing in the world that I've built, it matters that it is presented in the way I envisioned it
as an artist. (And yes, I do see world-building as an artform.)
It's not that I can't have fun with "these newfangled races," it's that I love the world I've built, and what is not in the world is as defining as what is.