Except accidental magic use in the Potterverse ignores all known rules of magic. It has young children manage things that aren't possible without extensive study and a wand. But even ignoring this, the facts that accidental magic stops when a child starts learning spellcasting, even in circumstances where it would save their life, and that children stop being able to perform wandless magic without super-advanced training, suggest it's not properly integrated into the rest of the setting.