Picture this: A BG where the Black Harvest and the Illidari are fighting, with the Illidari spaceship invading the Dreadscar Rift.
If you’re a Warlock you fight for the Warlocks, if you are a Pizza Cutter you fight for the Pizza Cutters and if you are neither, you can choose your side at queue.
That’s just one example, there can be plenty of non-faction based conflict 
There should be a BG where it is Demon Hunters against everyone else.
That wouldn’t be fair…for everyone else.
Fun idea for a brawl, but classes without a healing spec would just giga lose
Although my money is on the death knight meat grinder
It doesn’t need to be fair necessarily… there’s precedent for unfair encounters.
You’d run the BG twice and swap sides on the second round.
Well, it would also be fair for Demon Hunters too… They claim they sacrificed everything.
Deephaul Ravine is odd. It’s two factions of earthen fighting over resources that they both can access. It’s not like it’s hyper in demand or anything. They’re both on the same side.
Yet “hey you two factions of mooks, go kill each other, yeah you’re fighting for important resources go at it”.
I imagine Ruffious and Uljax are just having a beer, sitting on lawnchairs and laughing throughout the entire encounter.
I think its dumb that BGs are only ally vs horde, arena you play anyone, should be the same with BGs for faster Qs