Comment by svnt

It could send personal and significantly problematic emails to family or professional contacts.

It could change LinkedIn to add competitive work.

It could sign a married person up for dating sites and invite people to your house.

It could lie on your taxes.

It could attempt to join a terrorist movement or elicit other illegal activity on your behalf.

It could find many other creative ways to ruin your life and/or reputation, in the same brute-force manner as recent cybersecurity issues that previously would have required impossibly large teams of people.

Even if burning through cash is the only problem you care about, though, credit cards on Amazon is a small part of the financial picture for many people. Banks and brokers can be a much bigger issue.