Has anyone suggested random team round robin? So you would enter solo, but for each game you would be randomly paired with 1 or 2 other players. Each player would be teamed with each other player exactly once, and each player would fight each other player exactly once. IMO noobs would get to be in a lot more games, and it would stop players from getting eliminated immediately off a single unlucky game. It's also nice to have a change now and then, just to shake things up.
Round robin is normally very time consuming, but teams would cut the # of games down by a ton. If I've done my math right, 3v3 round robin would be more or less on par with 1v1 elimination, and I think that could be reduced further by removing players who have lost too many times.
And since each player is teamed with each other player exactly once, there's not much risk that someone will win by pure luck.