On Tolkien: The short answer is that Tolkien originally called the Noldor, Gnomes, having yet to invent the word 'Noldor', but eventually he decided that it was best to drop the word both because he rather would avoid the associations (already bad enough for elf), and because he preferred the sound of 'Noldor'. So, Gnome does not appear in any of the works published in his lifetime.
On Elves, Drawves, Halflings, and Gnomes: My wife fully agrees, and will probably never again play in a game world were any of those four appear on the grounds that any game world in which any of those four appear is severely lacking in imagination. Hence, because my D&D world contains two of those four, she isn't playing in my D&D world anymore.
I have no love at all for Halflings or Gnomes, and haven't had Gnomes in my campaign EVER and dropped halflings about the time I went to college.
In my campaign world, you may play Humans, Elves, Dwarves, Fey (several kinds), Goblins (several kinds), Orine, and Idreth.
If Elves are a reflection of a certain kind of delicate human beauty, Orine are a reflection of a completely different kind of standard of beauty. Culture is nomadic. Favored class is Bard. Many are Bard/Barbarians. Orine interbreed with Humans and Drawves. Although Orine and Elves find each other attractive, no offspring ever result from thier conjunction.
Idreth are 'born old', being mentally mature at birth. They have collective racial memories, are tall and thin with long gaunt faces, drooping mustaches, and hatchet like noses. They become increasingly stooped with age, but thier appearance is deceptive as they can be quite agile. Favored class is Wizard. Idreth are not particularly virile. New offspring are rare and they cannot crossbreed.
I cannot bring myself to lose either Elves or Dwarves (even to reinterest my wife in fantasy gaming) because those two are so archetypal. They are I think ingrained deeply in the human conscious, and occassionally a gene slips and someone with the obvious physical traits of either is born.
Of course, it's that gene slipping thing that makes it difficult for me to bear using Ogres in my campaign.