It is quite simple. You have a 1v1 (or maybe more) gamemode, where people pick the champs for the enemy.
For example: You and your friend, or maybe a random guy, decide to play a match of this mode. You can have bans, where you choose which champs you dont want to play, have as many as you like. Lets say 2. After those bans, you and the enemy chose the champ that you will have to play. Or to make it a little bit more random and interesting, you can choose between 3 Champions. Out of those 3 Champs, a random Champ is picked for your enemy.
All champs are enabled in this game mode or something similar to this case.
Why would this be interesting? Well, you could try Champs that you would never expect to like.
For example, in ARAM, I was given Yorick, whom i totally disliked. I thought he was pretty much the same champ after the rework, regarding his play-style of course. However, I was given that champ and I said... "whatever, I'll give it a shot." I would have never said or done that in any other gamemode. After the match, I fell in love with Yorick.
So let's say you seldomly play Kayle or Twitch and but you are given that Champ and you have to try-hard to win the game and get used to that Champ and his mechanics asap, after the match you may like it.
Of course there are many problem like: What if I encounter someone who has 1000 hours with Bard and I myself got Jax whom I have played an hour.
Just a thought...
tldr: A mode where a random champ is assigned to you, with which you have to fight 1 on 1.