Going back in time to before the official commencement of the Winter Wars tournament, a call for mercenaries was sent out to specific individuals within the Guild of Student Mercenaries, drawing together students that resided more in the darker and shadier side of the Infinite Academy.
It's not that Principal Khan and the Boarded didn't care to enact certain rules while they sit on their high horses in the light, but the foundation of the Infinite Academy had always been rooted in competition and strength. And if having an Underworld within the Academy helped foster that, but made student welfare slightly worse, then Principal Khan will happily take this trade.
After all, the reputation of the Infinite Academy had always been built on the shining stars that were the ridiculously strong Wave users, rather than the countless ones that fell in official battles or those that were expelled or ran away for one reason or another.