So what do you do? I strongly suspect a lot of you are going to say Siege of Orgrimmar progression, but that's a little dull. Challenge Modes would be made easier for sure, so maybe those too, especially given that your tanks could pull as much as they liked with no risk of death. I mean, so could your DPS, they wouldn't be in any danger either. But you'd still have to kill the mobs in time to get the medals, so it might be a little more entertaining than slowly whittling Heroic Garrosh down to 0 health.
Personally, I'd go exploring. No fatigue risk means unlimited flight range, and something about seeing the edge of the world appeals to me. And maybe I'd find the mythical GM Island... What would you do?