Harry Potter - The Underage Magic Trace was Useless Except for Orphans 

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It was a literary device that was used when it was convenient.

first they only care when magic is used in front of a Muggle outside the school, it does not matter if a student used magic in his own house infront of his wizard family outside the school. second Harry was only persecuted when he used an Advanced charm + in front of muggles. so a lot of small simple magic that doesn't attract attension can fly under the radar if it has no negative consequences on the wizard world since the main goal of thsi rule is to not Expose the wizarding world. But then by that logic. when Harry and Ron used the flying car, this incidents should qualify them one way ticket to Azkaban. damn nothing makes sense.