The Reason why they remove Triple, Rotation and Horde battles is because the lag in Sun/Moon, because the trainers being seen in the battles now.
Back in Black/White, Triple and Rotation battles made their debut, in X/Y Horde battles made their debut.
In X/Y and OR/AS Triple and Rotation battles were just as lagy as the double battles in Sun/Moon whiling the Double battles were in perfect shape.
Than when Sun/Moon come, they had to put the trainer in the battles now, but Triple, Rotation and Horde battles so lagy in Gen 6 that they have to remove all of them, if not the game would've crash everytime we do these battles (because like i said, the trainers being seen in the battles now).
and there you have.