Kouchi Uchiha is an anomaly made by Orochimaru that combines different genes of Ninja clans with some foreign DNA after Kagura's defeat. Without an origin and a idea of who and what he is, he lived as a Shinobi of the Hidden Leaf Village. He should have been the last choice to be considered for a mission about that new land of 'Magic'.  Hogwarts's request should have been looked after by a more 'normal' ninja, but unfortunately, he was the only genius who fell into that age bracket and had enough power to complete this mission. In hindsight, Kakashi should have made a better decision. But now that Kouchi Uchiha was at Hogwarts, he would make sure to leave his mark. And if a few people had to get hurt in the process, well, it would not be his fault.