I believe Riot stated in the Katarina lore rewrite thread that they didn't want champion backstories to focus only on WHY they joined the League, instead preferring to cover their most defining character moment. While that reason technically makes sense, it doesn't change the simple fact that the OP is completely right and we still have NO idea why half of these people are champions at all. So yeah, they've given their reason, but it's a BAD reason.
Rengar we know about: much like many champions before him, he came to the League to collect Cho'Gath's head (pretty stupid of him since there's an exactly 0% chance of the League letting him keep it, even if he DOES kill Cho in a match). Jayce is a traditional "defender" type who joined the league to represent Piltover, which is about par for the course for a character as boring as him. The Blood Brother's joined the League for the standard "represent my nation" and "show off how awesome I am" reasons. Diana, Zyra, Syndra and Varus have absolutely no business being in the League: Varus and Diana have personal vendettas that joining the League will do absolutely NOTHING to help them fulfill (unless they want nothing more than to non-fatally beat up on Noxians/Leona over and over again for thrills), Zyra would ideally be trying to avoid the notice of the Institute of War, due to their past record of imprisoning dangerous nonhuman creatures like Cho'Gath and Nocturne and Syndra doesn't have ANY agenda whatsoever apart from some half-assed desire to murder the leaders of Ionia because... I dunno, because Riot realised her lore had no depth whatsoever so they gave her some random, unjustified objective in an attempt to pad it out.
This is what we had League Judgements for, so we could actually understand our champions in even more depth than their backstory explained (like Lux's woobie-tastic "I have nothing else" story). But of course, that was "too limiting" so now we have to make do with jack squat.
Originally Posted by Sylph
I have full faith that the team is planning awesome things, we just have to be patient and keep up the support!