Wouldn't spending so much time training on the Fields of Justice teach the champions bad fighting habits? AD carries would get used to having infinite arrows/bullets/etc, tanks would get used to overextending and dying, assassins would take greater risks because they could just respawn normally, and so on. Annie's going to have almost no fighting experience in the real world; while she'll clearly be insanely powerful as an adult, she'll be making combat decisions off untrue premises. Even if you know intellectually that you need to be more careful in a real fight, you'll be fighting against instinct and muscle memory.
I don't really have a point about this, it's just something I've been thinking about. I guess, what do you think champions will do when the League fails and war comes?