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?

You must remember. The summoners are the real fighters. That, and they feel everything they do. Hm, not really sure how to write this.

The summoners are the most powerful entities in the world, they are the ones that need to be combat ready. The league was established to stop this. If they snag a few nexuses they can recreate the effects of the league for champions. So nothing is lost.

The champions themselves practice and have lives out of the game as well so they aren't constantly fighting under the given circumstances. So while if they lived in the league alone those things may become habitual but those that train are less limited by this.

That, and mages like Annie, and Syndra would need to be contained or killed in the instance of all out war because of the fact that the league was established to fight magical pollution which when power magic is used it is generated.