I like to think of the war school as a sort of "Charm" magic. Basically it can be used to inspire units to greater heights than they could have accomplished without some kind of magical influence. I would agree with you if there weren't some supernatural feeling spells that fit in the war school but a spell like Battle Fury definitely gives me the feeling of what I'm talking about.
As to your bashing comment, it didn't sound like you're bashing to me - I think it's totally valid to call into question the 'vibe' of spells as the creators have obviously gone through so much effort to make sure everything FEELS right. So I'm sure they're interested in this kind of input.
i can see a mage doing what you describe and having it be done as magic, however, it seems more appropriate for a battlefield and less so for an arena match.
When i imagine a mage using the war school as his main school, i dont picture that he is summoning or conjuring goblins or dwarves or what have you into the arena, rather they just walk in with him and he can make them stronger, which again doesnt seem fitting for an arena fight.