Anybody who's played ARAM knows how infuriating dodgers are.
Sometimes it takes 20 minutes just to get a game going from having 10 in a room because people keep randoming a champion they dont want to play.
Personally, I don't get why people play ALL RANDOM if they're not happy with what they pick at random.
Anyway, I think a feature that would help with this is Reroll. Once per champ selection, a player would be allowed to basically hit the random button again. This wouldn't exactly fix all the problems, but I think launches would go much quicker.
I also think it would lend a small bit of competitiveness to the format. Some teams are simply inferior to others. Allowing some small way of addressing the issue would be a step toward seeing ARAM possibly recognized as a legitimate side event complete with prizes at professional tournaments.