I voted for staggering, but I am reconsidering my vote. I think it does take some of the novelty out of this tournament, but at the same time, not IV staggering can put a crucial part of the game up to chance thus semi-defeating the skill aspect in select situations of this tournament. IMO, I think there should not be IV staggering because it does not put the teams on a level playing field, which if I'm not mistaken, is the purpose of this tournament. There is also practicality issues like Hidden Powers that Eric the Espeon mentioned earlier.
In addition, I might not have read correctly, so feel free to correct me if I am wrong, but the first person that gets to choose a Pokemon's IV to lower gets an advantage. For example, if I put a Scarf Jirachi on my team, and I get first pick at IVs to lower, I might make it so that my Scarf Jirachi can revenge anything on the opponents team, and will not have to risk a speed tie with even the opposing Scarfer. Building on this, if I lowered said Jirachi's Speed IV on my opponents team, and I have a DD Salamence, there is no way he can revenge it while I can revenge his Salamence with my perfect Speed 31 IV Scarfed Jirachi. Just something to think about I guess.