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No, it didn't have that many good ideas. The League seems like one, but creating factions you want to have cool conflicts and then creating an all-powerful organization whose sole goal is to stop conflict is self-defeating. It shouldn't have made it to the final game, but their story was hastily made to prop up their gameplay and they didn't really care (they didn't even care how well their game was programmed back then).
You know, they could also have interesting actions within the league system itself... Take Fiddlesticks, for example. Thing is though, they didn't
need these big overarching stories. Just cool little things on the side, like... I dunno, Teemo collecting mushrooms in some forgotten part of the world, and running into something crazy (like Rengar.) Of course, that's an arguably stupid idea, but they could have used it to flesh out the world's mythos and characters. Hell, they could have had some interesting stuff without even directly involving the champions themselves. It doesn't have to be
all about the champions.
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The JoJ was very unpopular, so there's that. And the realization they had was that the only big story they could tell in the old lore was "Two factions try to sneakily fight behind the League's back" so they killed it before it became repetitive. The Noxus/Demacia/Crystal Scar plot was pretty neat, but it wouldn't have the same charm the third or fourth time.
I'd say they've done a decent amount of great work fleshing out their world recently. Most of it is the kind of lore you can't measure with word count (such as making faction champs' visual themes more consistent) but it's still improved the game on the flavor front.
The thing you seem to be missing here... Is that the stories
don't have to center around the League or its champions. Tell us something from Runeterran lore, tell us something from its history or legends. Tell us about the kind of creatures that lurk the forest where Rengar and Kha'Zix hunted, or the deadly uses of the poisonous Shrooms Teemo collects. Integrate the League and its champions into things, but don't make (to take a way of speaking from the Angry Marines) 'ALWAYS CENTRAL ALL THE TIME'.
Then again, most members of LoL's community I've met seem to have the attention spans of a particularly rabid mongoose, so I guess that's asking for too much.
If by faction champs you mean 'member of the same organisation' like Garen and Lux from the Demacian military, yep, that's a good idea. If you mean 'members of the same city-faction' like Twitch and Mundo... Noooooope. Character's should have their individuality.