I understand your idea, but I still think they are and should be defined as marketplaces, with a scrutiny any marketplace should get.
The first reason is, Amazon isn't doing much curation (if any), due to their size they can't do proper curation, and bots are terrible at it (either based on keywords or reporting). This is proven by counterfeit items being sold, listings being stolen/manipulated, biased report systems.
Then Amazon claims they aren't liable for the products sold - the customer belongs to Amazon (you can't even have access to their names anymore), the listings belong to Amazon, everything except what arrives at the door.
At last, Sellers pay for the product advertising Amazon does, it's called a Referral Fee (ranges from 8% to 15%). In fact, the Seller pays for everything (and they should, yet the amounts are up for discussion).
So they have all the symptoms of a marketplace, yet Amazon plays what ever role is more suitable for them.
I only think they should be enforced the rules of a market place in any developed place in the world.
No real private marketplace would be open if they were selling counterfeits. Even if they sold legit products as well, until they purged everything counterfeit they would not be open, and they'd pay fines for it.
I bet if any public Health/Goods inspection force would be deployed on ANY amazon warehouse, they'd find shady shit. But such public organizations don't have the tools/protocols to do what they do in the real world.
I agree with you when you say, this isn't limited to Amazon.
For example, why can't we get the full data from the customer that purchases from us? Why can't they be our customer on Amazon? Amazon hoards everything, and we get the scraps.