This law isn't completely fair since it can't be determined who performed a spell, only that where it was performed. Basically, kids with magical parents can use magic all the time if their parents allow them, but muggleborns and kids like Harry can be blamed even if they didn't do anything. Also, many kids are mature enough to freely use magic long before the law allows them. There should be a test to determine whether the person is capable of using magic unsupervised or not.