It's actually not during Brawler. You don't need to be in tank stance for any of Brawler, least of all during orb phase when there are no stacks and the incoming tank damage is at the nadir of the entire fight. The only reason that I can see why you'd do this is if you're planning on letting one of your tanks go afk for that section to take a stretch break. I suppose speedruns can get tiring.

The bottom line is this: tank dps is about understanding the interplay between the defensive requirements of the fight and your need to maximise your damage output. Your defensive and offensive capabilities are intertwined. It has much less to do with complex rotations and a lot more to do with understanding patterns of incoming damage. If a player has an issue with with PLD dps in single target, chances are it's because they're not taking full advantage of PLD's superior physical defence and versatile toolkit to maximise their time out of tank stance. You can't be overcautious and still expect to do respectable dps.

Multi-target, of course, is a completely different story. My condolences.