So it's totally fine for a 4 year old to train a lv. 100 Raquazza.
You're forgetting something...nowhere does it ever say you need to have a license to have Pokemon; plenty of non-Trainers have Pokemon in the game. IMO, the only thing a trainer license would grant is the ability to compete in the Pokemon league, whereas anyone else can have Pokemon and even battle with them if they want, like the mentioned preschoolers.