This thread is like a culmination of all the talk about SwagPlay I've seen over the past few weeks lol. I don't ladder extensively, and I've only seen the strategy myself a few times, so for that reason I'm not actually gonna side one way or the other. The only thing I feel I can do is focus on the questions such a strategy brings up, though some of them have no doubt been presented already.
The main issue I see with SwagPlay is whether it is unhealthy for the metagame in the same way that certain other luck-based strategies have been deemed unhealthy. Obviously luck is everywhere in Pokemon, but no one bats an eyelash (rightfully so) on self-imposed luck (i.e., using moves with less than 100% accuracy). Luck-based strategies that are not self-imposed (i.e., confusing the opponent) are, by nature, never foolproof. There's always the chance the target doesn't damage himself right away, and he gets to apply whatever tactics he wants as normal. It's whether their applications in actual battles add an unnecessary element of luck that otherwise flies in the face of a more skill-based metagame. Evasion-boosting moves, for instance, can still go either way when it comes to moves hitting. But when they miss, it flat out gives you a free turn to do whatever you want - set up a sweeper, cripple their tank, kill a mon that otherwise checks you, whatever. All because of luck, not skill. More recently, there's Moody. Again, by nature it's not foolproof - the Moody user could get the boosts in stats that don't necessarily help it a whole lot on the first turn, thus letting your mons kill it as usual. But if it gets a boost in Speed on the first turn, all of a sudden it becomes able to Sub+Protect until it gets massive boosts in everything else, and then sweep through your team. Moody essentially boiled down to "if it boosts Speed first, you lost, otherwise you still have a chance".
The question is whether the luck factor that SwagPlay introduces to the metagame interferences with it to a similar level that things like Evasion moves or Moody did. Do the free turns granted through "priority" Parafusion, compounded with the extra damage dealt through Swagger-boosted confusion and Foul Play, mess with too many strategies too easily to be considered healthy? Again, I don't have enough experience to confidently answer that. This is merely my approach to the subject.
Also a minor nitpick to those suggesting a Prankster+confusing move complex ban in place of a Prankster+Swagger ban. Recall that damage dealt through confusion is based on Attack, not Sp. Attack. Swagger punishes the opponent a lot more for bad luck than any other confusing move, so I feel Haunter's initial proposal for the complex ban option works just fine there.