It seems like a lofty dream but....
people complain about premades in Unrated Battlegrounds NOW. And those have like 10-40 other people
now you want people to complain that people made premades for 2v2? I can see the forum posts now.
The big issue with rated pvp and solo que is the fact that winning and your rating is COMPLETELY dependent on the other people in said group
Solo Ques will NEVER win in rated BGs or will just be normal battlegrounds that matter a little. Meanwhile Arena oh lord that just sounds painful. I go solo que in a 2v2 have a DK in greens with a language barrier versus ...a premade. All solo que for actual arenas will do is make the lower brackets SUPER easy for pros and just a brick wall for people trying to do said solo queues