If a Pokemon does not use any moves that come off its Attack stat, it's beneficial for it to run 0 Attack IVs as it decreases confusion damage. Confusion actually uses your Pokemon's Attack stat in damage calculation, so removing those 31 points can be useful in certain situations.
It's also useful against Foul Play, and other moves where the opponent benefits from your higher Attack stat, such as Power Split (though you likely won't come across that move).
