Because their story was critically important to the story of LotR - in many ways I'd suggest that the failing of elves, ents, dwarves and the rest of the "old world" was the real story of LotR - the hobbits heading off to Mount Doom was just window dressing for that.
Here's the thing, though. A story has characters. An "age" isn't a character. It's a setting. Unless you blow the setting up to the relevance of a character (thus blowing it out of proportion to the human element), nothing should be "about" the setting. The elements of a story always involve a person: a person vs. god, a person vs. nature, a person vs. themselves, a person vs. a person. You could maybe try to tell a story about an age through allegory, but allegory frequently results in shallow characters.
If the story of LotR involves basically no actual characters, that is a severe weakness of the book and a deep criticism of JRR's writing.
Perhaps I give the man too much credit, but I'm willing to believe that the story of LotR is about the Fellowship and, specifically, about how a pair of hobbits walked from the Shire to Mount Doom (encountering all sorts of fantastic places along the way) in order to save the world from an evil that would make its wielder all powerful. It's about humility over hubris, about the triumph of willpower over temptation, and about, ultimately, how all evil destroys itself, how greed is turned back on the greedy, and how a lust for something as empty and soulless as power ultimately robs all life from you, but a friendship, a fellowship, and a companionship, can give you the power to take on anything.
That is, I think, why the story has endured and garnered such popularity, is the strength of that core story. It has persisted *despite* JRR's frequent skipping down obscure-self-referential-lore lane because there is only a small segment of the audience (the great clomping nerd segment.

) that is interested in that. It persists because he tells a very human story about the struggle of two friends in the face of overwhelming terror. Not because he chats about elf poetry.
Right. And RC, it strikes me that you're probably one of those who very much enjoys the worldbuilding. And you don't really seem to have any problems with your preference in your groups, so the advice probably isn't very relevant to you, personally. Worldbuilding is part of your fun, and it doesn't interfere with the rest of your group's fun, so no biggie.
But ronseur rather persuasively demonstrates that this passion for worldbuilding isn't always a good thing and, depending upon your group, could seriously bog down what is fun for them in what is only fun for the DM. So, despite the fact that the advice to have story triumph over world building isn't really relevant for you, it could certainly be good advice. It was given in writing, presumably, because in this professional's experience, like in ronseur's (and others who have posted in support of the idea), the general audience doesn't care about world details that aren't directly relevant to the action of the story.
A D&D campaign doesn't get the same exposure as a published book, however. It basically just needs to amuse the people who come to the weekly game (DM included), and so if all those people love to geek out on fantasy worldbuilding, the campaign is accomplishing it's goal of amusing a few people for an evening. Also, if you have no particular story in mind, tinkering around with the setting can sometimes help you see where a story can exist. And because PC's have more freedom than readers, it behooves a DM to prepare more than he will really need, in order to anticipate unexpected moves by the players. Which is why you will need more pointless world-building in a D&D game than in a published book, even if you don't particularly want to do much of it. Generally, the alternative is to poach liberally from published settings in such a circumstance.