Nah, it makes sense! Wall of text incoming here, I find this situation really interesting. ^^;
Riot wants to tell a lot of stories in this particular take on a fantasy world. They can't do that with the Institute of War around; it means all their characters have to come to the League in order for the game to make sense. That means the IoW has to be the most important place on the planet. So it has to be more important to Azir than, say, the ruins of his once-great empire he wants to rebuild, or more important to Ashe, Lissandra and Sejuani than their battles over the fate of the Freljord. Otherwise, they have no canonical reason to be there in the first place.
By having this one place you need all these powerful characters from all over the world to be, you need to make that place more important than where they actually come from. So, the rest of the setting more or less stops mattering - who cares about the war for the Freljord? Gotta fight on the Rift. Rebuilding Shurima? Guarding the Sun Disk? Sorry, gotta get a match in on the Rift. It doesn't make any sense unless you build your entire world and story around it, which Riot apparently does not want to do. They want to build a whole fantasy world, near as I can tell.
That's not even getting into how dying and killing endlessly would affect the champions themselves, how a bloodsport gaining international attention would affect the setting...it's a really big deal, and I honestly do not blame Riot for re-working their premise considering how all-encompassing the premise was.