Honestly, I think the "Dungeon Finder" set-up is the best solution so far. Longer queue times can suck, but it then makes you try other things. Like what was stated in the article; "How many people played Tank or Healer to get faster queues?". It punishes people for being narrow and rewards players who are flexible. The biggest downside for me isn't the longer wait times, I'll gladly wait a little longer to get a more enjoyable game, but rather the fact that creativity can be stifled.
We more then likely get Support Jarvan or Support GP because people couldn't get the lane but got their champ. So if you select a role, can you only select champs that are considered that role? What if I want to only gain ELO with 1 champ (Someone went to Gold with only Volibear this season)? How do I ensure that the player is playing that role and not selecting support to get faster queue times, but still playing whatever champ he wants?
"Dungeon Finder" is the best solution, it unfortunately has as many problems if not more then any other solution and for now would only solve the role call problem. Over time some problems can fix themselves (people will eventually play the "proper" character for the role they select due to effectiveness), but this will take an unknown amount of time. Honestly, Riot doesn't have a problem nerf batting champs into uselessness or "enforcing" the current meta, so maybe they should grow a pair again and just set it up. Mama always said: "You don't know how good it is until you try it".