A Title Much Cooler Than Anything on the Old Site
You could. Or you could assume that there are different distinct sentient, humanoid races, that can or can't interbreed and enjoy worldbuilding and roleplaying around what that might look like.Non-humans in D&D, and fantasy in general, are humans with funny-shaped ears. I have trouble understanding what the point in them is, they all merely represent subsets of humanity. It stems from the source - Tolkien. Tolkien's dwarves are dour, hard-working, hard-drinking Scots Presbyterians. His elves are his view of an idealised human - in harmony with nature, artistically-inclined. Hobbits are the rural English. You could do all that with humans.
I've been thinking of creating a campaign based on real-world archaeology. Set 50,000 to 80,000 years ago when homo sapiens was spreading out an encountering the neandrathals (homo neanderthalensis), denisovians (Denisova hominins), and Homo floresiensis (flores man). I like the idea of exploring that period when various archaic human began encountering each other and throwing in a bit of fantasy. You could look at this an argue that these are just different humans. But I think if you really get into the roleplaying and world building part of the game that this would be a very different flavor of game than an all homo sapiens game.
Also, dwarves, gnomes, elves, orcs...these races touch on some deep archetypes in our cultures. They may not be true to a specific historical folk lore and tend to be Tolkien-influence mash-up of different folklore, but the early creators and players of D&D and the writers who influenced them tapped into some powerful archetypes that remain compelling today. I like a surly Scotsman as well as the next, but he's not a D&D dwarf.