Well, most of times it' s said clearly why a determined champion joins the league: for example all the Void related characters join in order to consume alien forces ( in particolar Vel' Kroz wants to "consume knowledge" ), others because they seek challenge ( Rengar, Braum ), others for political influences ( Alistair, Ashe, Lissandra ), others for military propaganda ( Elise, most of the Noxians), others do it for their own pleasures ( Aatrox, Kartus, DRAVEN ) plus miscellaneous as gathering information or knowledge ( Yasuo, Amumu, Xerath ) or training for a later objective ( Gnar ).
The problem mostly is why the Institute, if it still exist, allows them. As far as i know they aim to be the absolute neutrality, and sometimes ther emight be a puppetmaster behind the scenes that can allow things, but also about extraplanar forces? Most of times it' s said that some champions are rather caged by the League and used in the fields of justice in order to keep them under control ( Brand, Fiddle, Nocturne, Renek) but it suffices?
About story developement, for obvious reasons it can' t develop very much: the story of the game is in the moment you join, and does not carry over for successive matches. Ashe might become the queen if you win against Liss or Sejuani, but that can' t impact successive matches for obvious reasons; for the same reason they can' t end the war between those 3 even lore-related, else they will lack a meaning to be.
With these premises, story developement can be really really narrow: besides few things like Kalamandra, Janna' s leaked nudes, the Pentakills, fanservice about weapons ( how much red steel is present in the Executioner ' s Calling? NONE BECAUSE NO MORE GIVES LS ) aren't really pleasant to read and all looks like filler, even if in the whole the idea is good; it' s the case of the Journal, and you see how it ended, even a big reader like me could not handle all that!
Other stuff like Frejlord events, the Ionia' s liberation war and such are cool things that can' t be done very often else they become rushed and with less value.
They are destroying little bits of lore, just to get a better base next. Don' t worry for a total overhaul, for that you need to wait LoL2 where then they will be able to change stuff from the basement.
