I think it could work the same way it works in Starcraft 2.
When you solo queue in SC2, you come across guys who joined your game just to troll you and cause you to lose your game. You get guys who disconnect / never even show after the loading screen. You get guys who suck. And it still feels balanced because by the end of the season if you and another player both played 300 games, you both had your fair share of good players and bad players, as well as ideal comps, and vice versa. The better player however was generally able to pull off more wins, and win more impressively, and a rating is determined by this.
While it could be an entirely separate bracket from pre-made Arenas, you could also have solo queues play against premades, but have it set up the way SC2 has it set up. Have 1800 rating as solo queue be the equivalent as 2K rating as pre-made queue etc. With enough participation you could even have bronze, silver, gold league etc.
Would anyone else think this is fun, or is it just me?