Yes, I'd absolute love it.
Yes, but only if the queue times weren't too much longer than they are now.
No, the system is fine now.
No, it would drive up queue times enormously.
It currently IS like that according to blizzard multiple times, with the down-grade thing built in. According to what I last read on em, the random BG finder will try to match you up with equal-ilvl players if possible, but will rapidly put you into groups with lower ilvl players to fill up group. Thus, lets say that 20 550 ilvl pvp players qued up almost at the same time, the tool would attempt to put them all into the same BG, but prefers putting players into battlegrounds fast over matching ilvls.
I do arenas, not so much this season due to schedule conflicts, but I just look at random bgs as like an lfr to help me get some quick honor or push me to cap my conquest if I only need a little more. Or when I'm bored and want to go for some achievements. Nothing more. The rest of the teams ilvl doesn't mean a thing to me, when it comes to loosing that isn't the only contributing factor. Skill is more important then the gear.
I just started pvping with my mage who had 0 gear, all pve, and could hold my own pretty well. Obviously as I got pvp pieces I noticed I didn't die as much/quickly. But I was still doing pretty well.
Remove factions first so that it wouldn't break queues and it would be fine. They could just use some phasing gimmick to make other people on your team look like your faction so that the HvA feel would remain.
Then again, that sounds an awful lot like work, so let's just make some minor U.I. changes and call it a day.
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I already have long enough queue times as horde. Wouldn't really want to see that increase >.>
Why should my ilvl make a difference? Maybe a bracketing based on PvP power or something, but bracketing solely based on ilvl would allow PvE players to queue into the max bracket since they get gear that has to be detuned to be suitable for BGs.