Yeah, I agree with Jeirien. They're orphans. True, they have limited manpower for the war against the demon beasts, but they also have limited manpower for teaching the kids, much less CAPTURING varying levels of demon beasts and setting up the training regimen that you guys describe.
As for why they didn't send them somewhere with weaker beasts... What makes you think they didn't? They were fighting fucking rabbits and songbirds at the beginning. The fight then attracted a few larger ones that wiped the floor with them.