A lot of what's "towering" is towering because of institutional taste, political circumstances, etc. - in a word, historical contingencies. I went to a fairly liberal university and most of my professors really disliked Eliot - not because of his poetry but because of what they perceived as his literary and cultural elitism. So it's not always a question of aesthetics or taste.

Another example: Keats is nice, but Browning and Tennyson are much better in my opinion; however, they were so lionized in their own time that a reaction against them set in during the early 20th century (one reason why Eliot, Pound, and others did what they did and became famous for it).

In my opinion/experience, exploring literature (same with art and music) begins with personal response, personal taste, personal resonance. At some point, many readers become more curious about works that they feel they don't get, but that others do. Some readers go further and start looking for totally fresh work, so fresh that no standard judgments have been set for them.

It seems to me not so much "chip, chip, chipping away" at them, but more like entering and exploring a new landscape, climbing a few hills to get a better view, then hiking through the woods, checking out the flora and fauna. Up another hill to get a view from another angle, and down into the next valley.

"Lyrical Ballads" is a good example. Many people have a basic idea of what Romanticism is or was, and can enjoy Wordsworth and Coleridge quite a lot. But if a person learns more of the historical and philosophical background, then more of the resonances and meanings of the poems appear, and their sound is a bit clearer.