So the competition was to select students to recommend to the military. The top rankers would be given a chance to participate in training with the military. The students would get some exposure that would help later when they apply to the military Mech squad as well as the opportunity to pilot real Mech's.
So in other words this is a reward/incentive program for the students, and a selection program for the school to recommend to the military.
That being said these students are to be w/o a doubt the "Best" the school has to offer and carry the reputation of the school. Even though the MC won the right to participate the school does not feel comfortable sending him as a representative. If the school truly had a problem with his fighting style they should have said or done something sooner. Like changing the rules of the matches to favor close combat, or outright banning it altogether. Or they honor the tournament and change the rules for next time. You do some thing before or after not in the middle.
Imagine the first kickboxer being disqualified from the finals of a boxing tournament for using his legs. Despite entering and making it to the finals no problem.