Personally, I've always hated game modes like that. They have the same sort of thing in Smite and I always refused to play it after the first few games because it just wasn't fun.
But, my personal feelings aside, I feel like this sort of thing is difficult to implement. Riot would have to decide if you could only pick champs you owned or if you could pick from them all. Then they'd have to decide if the champs should be randomized across (how I usually see things done) or if the players should be allowed to choose like you're suggesting. Being able to chose would be a bit more fun but then you'd end up with having to have some sort of pick order and I feel like that would end horribly with people arguing about what champs they wanted. Making people have to pick from the lists given in the client for each lane would make things a bit better I suppose.
Overall, no matter how they did it that kind of game mode has never been something I enjoyed, though I'm guessing plenty of people thought it was fun considering its something that seems to show up at some point for MOBA games.