Yeah, that works too, until it is damaged, lost or, stolen and you try to collect the insurance. You have to describe the loss. Insurance will not pay because you didn't follow the proper procedure when you shipped it. It will probably involve the ATF at that time.
Please point out in the USPS regulations I've linked where it states that I have to declare I've shipped a firearm. If the USPS loses the package, how would they even know I shipped one? And the ATF only cares that I follow the 1968 Gun Control Act.
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