Even if it is not a matter of AML regulation, if he buys physical goods at some point he will have to provide personal information, because how will he get the product he bought.
~snip~
Theoretically, he can use the PO Box to deliver the products thus purchased, so that the seller does not know his personal information. This is a good way to protect privacy, although when you contract a PO Box service you have to provide all your information, so it all depends on how much the service provider protects the user's data and thus their privacy.