Besides, the rules around country of origin are complicated, and some countries have product description law about this. And what's to stop Amazon sellers sticking fake country of origin on, as they can already do for CE marking?

Or the reverse: Amazon stick a China flag on iPhones. Apple are going to get extremely upset about this and sue/offer money to change that to a US flag.

The https://en.wikipedia.org/wiki/Israel_Anti-Boycott_Act may make it illegal to force Israeli sellers to identify their country of origin.

Who declares the country of origin? Who ensures compliance for item? How is compliance done? Do you review every single item?

How do you ensure that manufacturers update their country of origin declaration if/wehen they change downstream procurement? If you the raw materials are sourced in China and assembled in Vietnam, does that count as a Vietnamese product?

Amazon still has trouble with fake reviews, brushing scams, and straight-up counterfeits. Adding another system that needs to be policed doesn't seem like a very good idea. Especially when that system (country of origin flag on every product) has questionable upside.

Amazon has also become almost as bad as Alibaba in allowing counterfeit and knockoff items to be sold openly.