One word: switching
In competitive battling, everyone switches their Pokémon around, Justified is a great ability that takes advantage of this, as the only Pokémon with Justified are all Fighting types, so most of the time they can safely switch in and gain an Attack boost. It also deters opponents from hitting Pokémon with this ability, unless it is Keldeo which almost always runs special sets. Those are ways it can be useful in single battles, and as you said it can bring you all the way up to +6 in double battles with Beat Up, and is even possible in single battles with prediction.