Lore-wise, I think Fiddlesticks has some potential for carrying the story about peasant folklore in Runeterra. That could be an interesting niche to explore. I can see him being something like Janna, brought into existence by people's prayers, but it would be more based on childhood legends and fairy tales. I do predominantly ARAM games, so I can't speak for the Rift, but on Abyss, his E and R are kind of nice to have around on your side/a pain in the rear to go up against.
For Corki, it's too early to say about his lore. We really need a more updated view of Bandle City overall. He could still have a place there. As for his kit... We already have other bomb throwers (Ziggs, Zilean), so his Q could be replaced with something more unique. I think some version of Corki's R could replace his Q. Missile attacks seem more appropriate for a helicopter anyway. The new R could toggle the 'package' on and off, rather than waiting for it to be available (it might need to be nerfed a bit then). He would be somewhere between Nidelee and Karma in that his R 'transforms' him to enhance/modify his other attacks (though all would remain range-based, of course). Personal gripe: for his E, it would be really nice if you could lock on to an enemy or at least a direction and then have the bullets keep firing in that direction, even if you turn. I feel that I waste a lot of that ability as I try to maneuver during fights.
Nunu is probably my least favorite champion. His kit is underwhelming, and visually/vocally, he comes across as a character lost from Dorra the Explorer. I get that Runeterra has its 'whimsical' aspects so it's not a totally grim-dark setting, but Nunu kind of pushes that for me. Like dropping Aang from Avatar into Middle Earth. Freljord especially seems like a more serious-than-normal region in this world. Lore-wise, I think this is an occasion where it would be appropriate to go a little darker with the character. Maybe have the kid riding the yeti be Annie's lost brother, or perhaps a yordle who ended up in Freljord (we have yordles for Piltover, Ionia, Demacia and Noxus already). Or, the kid could be Braum's son, which would give us the first parent-child relationship in the game. For story, I could see Nunu having found some key or object related to the Watchers, and trying to bring it to Braum before things get out of hand.
So back to your original point, I don't think getting rid of champions is the way to go. If they already have established characters, it's probably easier to do reworks and updates than to create something new from scratch. And besides, even though it would be years away, Riot will probably run into a point of 'champion saturation' someday. At that point, they would have so many champions that it's no longer economically feasible to release new ones and maintain the old ones. Plus, if they cannot grow the player base fast enough, the amount of time that players spend on each champion will decline if the number of champions increases. It becomes a choice of pouring resources into something new that will shrink how much use everything else gets, or of modifying and updating things that already have an established place in the game and story and that at least some people are already using.
But if I had to vote, I'd pick Garen. Just... freak'in Demacia. Hope the whole country gets swallowed up by the sea.