Broadly, and with caveats, Amazon could somewhat trivially prevent much of this by requiring authorization from the customer who originally uses a shipping address, before allowing someone else to use it.
I know BestBuy.com is able to do SMS 2FA with my Bank of America Visa credit cards.
Maybe that will happen at scale if more card issuers decide the inconvenience/friction to legitimate card users makes it worthwhile per the level of fraud they're seeing.
But, the solution to the address problem here assumes the current state of things.
And, there are other issues involving addresses that strictly validating the credit card wouldn't solve (like unsolicited package and brushing scams), as well as things I'm sure we've yet to consider.
In general, it would probably be a good thing for people to have better control of who can send what to their address.
Heh. I knew that'd be the first question.
Yeah, that's one of the caveats. The auth email or SMS to the previous owner would allow them to indicate they moved. That would probably handle most cases quickly. But, if no response in x time, it could default to allow and/or if the new owner wants to be proactive, they can send proof of residence. A little bit of a PITA, but doesn't add much to the PITA moving already is. And, moving is pretty infrequent.
There's also billing address validation, as that frequently matches shipping address anyway.
This kind of validation would also help with other scams.
VisionPlus or one of the many other systems that may be employed in the chain of payment are configurable for many many such triggers or rules, change of address IIRC is a pretty basic one.