I believe it started as a reaction to the teaching rigidness and the over-reverence of classic texts by previous generations, people just got fed up. But more importantly there's now a variety of texts that explain, enhance or abridge the classics in a more approachable manner and an overabundance of new knowledge and art to explore.
However, there's still lot to earn by reading the original texts. I reread the Iliad and the Odyssey in my late twenties and I felt this fuzzy feeling of familiarity, that human nature hasn't changed that much (if at all) through the ages. Wrath, love, courage, friendship, betrayal, revenge, vanity, wisdom, ingenuity, stupidity - way too familiar.
One of my favorite parts of the Odyssey is when Odysseus' dog recognizes him. In a few words Homer describes the special bond between dogs and humans, a relationship that spans millennia and keeps strong even (more so) to this day.
As far as things to skip due to an abundance of choices go, those are perhaps unwise ones to avoid, if some part of the other "paths" you'll walk include pretty much any other areas of Western art.
Maybe you decide your "path" is 19th century French literature. Guess which two bodies of work are foundational to that? OK, so you just like sci-fi. Well, there are the Bible and the Classical writers again, at least in the better stuff. Medieval studies? Yeah, obviously. Film—like, pretty much any of it that comes from the West and has artistic value? Oh god, yes.
Well screw all this, I'm gonna focus on Arabic or Persian works. Oh. They have significant cultural ties to the Greeks too, thanks to Alexander, so I'm back to that again.
Fine art. There aren't even words so I'm safe there. Oh, wait, no I'm not. Damn. Music? Ugh, there's Achilles and Abraham and Aeneas and all the rest. Philosophy? Nope, too much of that assumes the same common, smallish set of common experience as everything else.
OK, fine, I'm so over this, I'm just gonna play video games. This Deux Ex thing is supposed to be good for some reason, let's start there. Oh... oh no... not again!