The Institute of War Encouraged Interesting Champion Interaction.
Looking at some of the more recent champions that have been created without the Institute of War or the League of Legends as a part of their backstory, it seems to me that the removal of the Institute of War has led to some of the most bland champion lore we've seen in awhile.
(Sion's lore was cool...but that was a retelling of an older champion's lore, one who was designed with the Institute of War and the League of Legends in mind. That being said, look at how much better his new lore was than anything else that has been produced this year).
In my opinion, the absence of the Institute of War and the League of Legends from LoL's lore has led to these characters being a bit more boring than they could have been. Here's some examples that come to mind:
Gnar - Wouldn't his character be more interesting if he actually mattered? Just by spending a bit of time at the Institute of War, he could get some face time with some of Runeterra's most influential people, and actually have an effect on the world. That is not the case post retcon.
Nami - Her story could be much more interesting if she could interact with a bunch of her fellow champions, and draw upon the resources available to her at the Institute of War.
Yasuo - What if Yasuo used the Institute of War as a safe haven for his supposed crimes, while he figured out who the real killer was so he could clear his name and return home. By being at the IoW, he could interact with any of the other champions (in a friendly or not so friendly way) and try to figure out what happened in his back story. Sounds like a cool on-going mystery to me!
Azir - He could use the IoW as means to semi-peacefully re-establish Shurima as a nation. Imagine the political stories that could be written with him meeting with key political figures such as Swain and Jarvan IV, all while trying to be recognized as nation by the world at large.
Also, let us not forget about the lore gutting that Jax, and many other champions like him, are currently doomed to receive due to the lore retcon.
In my opinion, removing the Institute of War seems to inhibit Interesting champion interaction within the lore.
using the IoW as a haven would more or less destroy the tension,I mean he would be perfectly safe living there,he wouldn't need to worry about ionian assassins anymore and with the IoW it should be actually rather easy to find more wind-users who could have been the culprit
s quest to find the moonstone would be greatly simplified with her more or less just sitting in the IoW,doing matches and waiting until the summoners find her some information about the moonstone,because they have simply so much more resources than her.
can and most likely will meet up with the leaders of the different nations,I mean he doesn't want his kingdom to be overrun by its neighbours.Now however we can't predict how the nations will react to azirs rebirth,they might attack him,they might want to establish peace with him,they might offer him help,we can't tell.Before with the IoW it would have been basically "Azir walks to the IoW,he joins them and his kingdom gets protection"
is a good point,the little guy has now no real reason to leave the jungle,but then again,he is listed as a friend of lulu and heimerdinger,so who knows how he met them.However I doubt that gnar would have had much influence on the really important guys,I mean gnar isn't really smart and seems rather naive,so yeah I dunno what kind of big role he could get even with the IoW