I like the idea of these people being scouted. Perhaps the actual 'Valkyrie league' is more like a goal for the players. When they finish training, that's where they will go. In the meantime, they're all in some smaller 'league' for people showing a lot of potential. Still doing professional matches and entering tournaments, but on a smaller scale. A lot more focus on training and friendly rivalries, like you stated. That does feel a lot more like the genre we are going for.

Could the first arc be leading up to like a freshman tournament?