While they can detect underage spell use, if I remember correctly they canonically cannot detect the type of magic being used. Perhaps it would have been possible to set up spells to detect types of spells in use by adults, perhaps not, but I think wizarding norms on privacy and individual rights probably would make it politically unviable in any case. Remember when Harry offered Minerva his wand when he was going to be staying at home, and she responded that "that isn't done." Wizarding minors aren't allowed to use magic unsupervised, but even muggleborns at home with no adult wizards are still left the use of their wands. That strikes me as a society which has some very strong norms about autonomy.