Yes, addresses are a huge anonymity problem. You can still use things like PO boxes, but it is illegal for someone to recieve packages on behalf of another person without verifying their identity. There are easy illegal solutions, for example, your friend could give a false name and trick an ignorant stranger into accepting packages for them. Or your friend could ask you to mail a gift to the address of an empty lot or to a stranger's address, and then "steal" their own package off of the other person's property. But the best legal solution I've found is using Amazon lockers. Ask your friend to tell you the general area where they live (EG. city, state...) and then order an Amazon product to an Amazon locker near them. The only real limit to this is that you would only be able to send your friends Amazon products. What do you think?

It really depends on the threat model. There are "discreet" remailing services, that promise to only give your information to law enforcement. For example, PO boxes are pretty convenient for US residents. But if they don't want their information in the hands of ANYONE, then I promise you that Amazon lockers are by far the most convenient possible legal solution for US residents to recieve packages without giving an address tied in some way to their identity. I've looked into using hotels, self storage units, and even homeless shelters as places to accept packages without an ID, but I've read the law myself. It is a federal crime to accept someone else's packages without obtaining their ID. The only exception is if the packages aren't sent by USPS or to a USPS addresss, and the only people big enough to create an alternative network are Amazon. Otherwise? You are better off just flying over their yourself.