Not necessarily. They don't need to be fully trained in both schools. That being said, all mages need weaknesses to counterbalance their strengths.
Also, if primary schools were only mixed together for extra powerful mages, we'd probably run out of new regular mages very quickly relatively speaking.
If each major school has four mages trained in no other major school (2 original + 2 alternate) That would be 24 mages. If you include an Elementalist that makes 25. If six mages are released per year, then that means Mage Wars would only last a little over four years before they stopped making new regular mages and abandoned them for archmages.
Also, what about the Paladin? He's probably going to be trained in Holy AND War. It just doesn't make sense for him to only be trained in Holy plus am elemental school.
Speaking of which, I wonder why the malakai priest wasn't trained in fire. I'm going to start another thread for that.
