How to work the league back in and still have it not affect anything

So its been awhile since the removal of league,the summoners~~,anything half decent about the lore~~ and i had this thought rattle in my head ever since then and i felt like writing it down here right now,for some reason.

Okay so instead of having the league be like an effective UN that has removed war make them like a real UN whos only job is to take in strays(riven Rammus,Lulu,Veigar,Yasuoe etc) and to keep the physical gods in check(seriously why haven't cho'gath 'kha'zix vel'koz rek'sai and malzhar not taken over the world yet or are they fighting against lulu veigar and gnar who are themselves fighting azir nasus and sivir who are in their constant war with cassiopeia renekton and xerath(all of these champion groups i just listed could each destroy cities with out much hassle if they wanted)) and league battles could be a false showing of friendliness among the factions