You won't find any official relationships outside of Ashe and Tryndamere's political union, but there are a plethora of hateships.
That's an interesting thing to notice about the champs. I wonder why Riot is so hesistant to make the various fanships out there a little more concrete? I mean, it can't possibly hurt them to do so at this point; everything's getting re-written, why not go crazy?
League is teen rated and romances generally imply adult themes, so they don't showcase them. That way they don't have to hear who know how many associations of conservative parents screaming that it's a scandal the portrayal of romance in a game directed to children as well.
Besides, just imagine if they set someone as not being heterosexual and in a relationship with a same sex character: BOOM, the perfect assist for reactionary associations who just want to bitch about things and videogames in particular.
By implying things only, they achieve to give tidbits to those who are interested and at the same time avoid these major hassles.
I don't know. They show relationships between characters on the Disney Channel (pre-teen and teen shows), and there are movies directed at the pre-teen/teen audience that also show relationships. I wouldn't say it's an adult theme anymore, but that certainly depends on how it's presented.
But you do have a really good point.