Arena and RBG is rated play. And the thing on Timeless Isle is more of a "I want to kill everyone", not just same-faction shenanigans. Implementing same-faction random BGs would be the last nail in the coffin for any chance the Alliance might have to make a recovery from the exodus that has been happening over the past year or two.
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People have been mass-switching to Horde in recent times, leaving Alliance with really crappy win-rates but with exceedingly fast queues in comparison to Horde.