Unfortunately, that’s only your word. The way this system is designed, nobody will notice if Amazon chooses to be less obsessive about it. Or if their systems are hacked. Are you certain that these web services are secure? I’m not (one obvious vulnerability has been reported). If someone compromises one of these services, the results will be disastrous.
Speaking for myself, not the co: we all decide who we want to trust and why, whether it’s browser extension, or a browser, or a phone.
For me, it comes down to alignment and value. Amazon stands to lose a lot if they decided to suddenly stop caring about customers, or not take security seriously. And the Internet gets pretty small if your threat model requires zero trust.
I work on a shopping assistant type browser extension and I am very confident that if I proposed an architecture and implementation such as the author identifies here I would be turned down immediately: having good intentions around privacy is one thing but deliberately designing your application in a way that allows to bypass almost entirely the review process required on submission to the store is something that should be answered for.
Note: I am the author of the article above.