Competitive, by definition requires the ability of competitions. If I can't set up a bracket and make a tournament with teams, it isn't competitive.
As someone that doesn't get into competitive gaming, even I understand this.
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It's always possible Bungie kept this option away from players in order to control the competitive bracket system through another time controlled NPC such as Lord Saladin. Nothing has been confirmed obviously, but this could be something that Bungie might be hiding up their sleeves.