There might no Underdark. Every dungeon in the world could be above sea level: in the mountains. Every mountain could be riddled with stacks and stacks of dungeons, goblin caverns, and general mythic underworldliness.
I get the feeling that that’s the case in Tolkien’s world. The dungeons are all in mountains: Bilbo’s goblins, the mines of Mordor, the Lonely Mountain, Mount Doom. There is no chance that there’s a dungeon under the Shire or Rohan.
If you jam-packed a mountain with mythic underworld, what would its population be? As high as you needed — or higher. Manhattan is 33 square miles, and, generously, 1/3 of a mile tall from the base to the tip of the Empire State Building. Mount Everest is about 580 cubic miles. That means you could easily fit Manhattan 50 times in Mount Everest. Everest alone could fit 75 million cosmopolitan goblin residents, and up to half a billion goblins during the weekday (commuting by goblin subway from less desirable mountains).
OK, that upper limit is pretty ridiculous. But we can safely assume that, if the mountains are reasonably well-riddled with dungeons, there are many more monsters in the world than there are people.
Fantasy is, in my opinion, a conservative, maybe even Tory literary form, and a direct descendant of the British imperialist adventure format familiar to many early fantasy writers. (Sir Richard Burton was a relative of Lord Dunsany. Tolkien was born in South Africa, and mentioned H Rider Haggard as one of his favorite authors.) The premise of imperialist history/fiction is this: a handful of civilized people set out into the wilderness, and, through superior organization, defeat overwhelming numbers of native peoples. It’s usually accomplished by neutralizing barbarian leaders who could bring about the ultimate disaster: uniting the numerically-superior hordes under one banner. That’s what Aragorn and Gandalf are up to, and it’s also how the British saw their role in India, Africa and the Middle East.
The role of civilization in D&D is no different. Adventurers go out and kill goblin kings and evil necromancers before they can gather their power. (This theme is complicated by the Howardian branch of American fantasy which pits, not civilized folk, but barbarians against the wild. D&D is big enough for both strains.)
The mountains are a nice place for this imperialist war against chaos. The mountains are nicely laid out on the world map, not like subterranean Underdark which requires a separate sheet of paper underneath. They’re impassable; they’re strung together in great malignant walls; and they loom on the horizon like thunderclouds threatening to spill forth a storm of war onto the world.
With so much room for evil in the mountains, it makes me wonder what’s under the good honest dirt of the Shire and other civilized places. More dirt? Hell? Sunless seas sailed by the dead gods?