I dont see where it would feel too “coin flippy”. Its already coin flippy just 6 rounds of it. Most games seem decided by lobby. if you are the only caster in an all melee lobby, thats going to be rough for you, probably 2-4 or 3-3. On the other side of the coin if you are one of three casters with a melee in your lobby then you are almost guaranteed a 4-2 lobby.
Lets also not forget the lobby dog, thats gauranteed to go 0-6. Also if that lobby dog happens to be a healer, youre not going more than 3-3.
Honestly, I dont see how many games are decided actually during the arena.
I think having Solo Que be Rated Skirm 3v3s would be way better. Healers would still instant ques, wouldnt have to sit an lobby where they are guaranteed to 3-3 for 20 minutes because one DPS is a lobby dog. DPS ques would be way shorter, no longer than a random BG.
If a Solo Shuffle takes about 20 minutes, and on average you are in que for 30 minutes, and healers being able are the reason you are in ques so long; its fair to presume those healers are in a game. So if you cycle them through lobbies faster, instead of 20 minute lobbies the lobbies are 3 minutes, your que times as DPS would be about 10 minutes. Slightly longer than a random BG if you play on the populated faction.
Theres also the option to put Solo Que into the 3s bracket artificially inflating participation in the 3s ladder. Obviously rating would be separate, but you could actually play in the 3s ladder. Now before you say, well the other team would be in coms/coordinated/optimized, which is fair, everyone would be have the same experience in solo que so it would average itself out with good comps and bad comps.
Also just a side note here, Solo Shuffle already has unoptimized comps. As ENH the only caster that is a viable comp is with Demo lock because they have MS. If I que and get a mage, boomie, ele in my lobby, none of those comps are optimized for my spec.
Just food for thought.