From a literary point of view, I think Rowling introduced the concept of the restriction of underage wizardry in order to carry out certain plot ideas (i.e. Harry's not able to defend himself from the Dursleys, to free himself from his room, has to face the hearing in OotP etc.). Within the magical world, I think that though it is forbidden for kids from wizarding families to do magic, they hardly ever get caught, as the Ministry can't tell whether it was really them who performed a spell. If, however, they are caught, they will be punished.