After the completion of the Izuru Kamakura project, due to the non-existence of a personality, the project leaders decided that it was a failure, so try to hide their project by enrolling him at the academy, but also hope that maybe interacting with students may yet make a personality fester. AU if it wasn't obvious by now.

What if Remus hadn't forgotten to take the Wolfsbane potion the night Wormtail was discovered not to be dead? What if Sirius was now a legally free man, not stuck in hiding? See the butterfly effect in action as Harry's subsequent years at Hogwarts are very different to what is known.