But retails also sometimes operate under the model where the inventory on their shelves was purchased by them from the manufacturer or distributor. They are taking the risk on the inventory, and not selling means they are losing money. The manufacturers and distributors were already paid.
So, I reflect a question back to you: If it's all your owned inventory, what does it matter what name is on the box? No matter what, you the retailer are getting your sale and making the profit. This is not true of the marketplace model. There, whitelabels are directly competing for every sale, and no sales means no money to the manufacturers of those other products.
All this is also heavily discounting the fact that Amazon also owns the search. Some people equate this to product placement on shelves, but it's really more like there's two stores. The first store is all Amazon stuff, and you have to walk through that store to get to the second store, where other sellers are.
You've taken a relatively rare thing like slotting fees and built up an entire mental model around it. That would be like saying that all programming languages are typeless because you heard that JavaScript isn't typed.
2) When a supermarket takes on Brand A cereal, the Brand A owner makes little risk, they get paid whether they sell or not. The supermarket is taking all the risk. If they bring their own store brand, they still run the entire risk, now for both stocks. If cereals stop selling well (because there is a milk shortage) then the supermarket is loosing a lot of money. Amazon faces no risk, they can have the vendor for Brand A continue to sell non-prime cereal from their own stock so amazon faces 0 costs if it flops. If the vendor does well they can be onboarded for inventory management and prime shipping, amazon takes more risks and more profit. Lastly, they can use methods like "We suspect the product is counterfeit, send bills for when you bought it" to gain direct access to the manufacturer of Brand A. Now they can sell Brand Amazon directly from the manufacturer, leaving the Brand owner of Brand A in the dust by selling the same product, that did well, cheaper and hiding them in the search results below their own.
The supermarket equivalent would be that the supermarket subsidizes the Brand A seller from their value-add in-store things like customer payback cards after a while, then blackmails them into giving them the manufacturer by threatening to not sell their popular product, then selling the manufacturer's product under an in-store brand and the Brand A cereal is only available under-the-counter. Brand A seller is also entirely co-dependent on the supermarket as that supermarket is 90% of the market.
I know you have wallmart in the US but in the EU we do have some variety in supermarket chains (ALDI Süd/Nord, LIDL, Edeka, Rewe, etc.).
One difference is the branding. Grocery store products rely far more on branding, and slotting fees are often used for market research.
Stores cannot reproduce the branding, therefore their own-brand products don't have the same competitive appeal.
Amazon actually hides prominent branding. A few big brands have their own mini-stores, but most of the time you can't tell if you're getting a product from Amazon, from the original manufacturer, or from a retailer.
So when Amazon uses market analytics to decide which products to make and sell, it has a huge advantage - and it can and does wipe out existing sellers. Which is something grocery stores don't do.
Retailers are also NOT interested in buybacks, as the cost of shelf life is not cheap(much more expensive, than warehousing)... and white label products are also higher risk(not shared risk) for the retailers and are always lower margin.
There's a very clear difference between financial incentives between traditional retailers and Amazon. Equating them - is ignorance at best.
I think amazon is better compared to the whole street where the stores are, than to any store.
CVS (or really any large retail chain that sells 3rd party products and produces their own) is in a similar situation. One could, and rightfully so I think, make the argument that CVS etc should not be allowed to produce their own products, because they have significantly more insight into what is sold. Amazon noticed that several products were selling quite well and decided to get a piece of the action. Beyond showing their own products as higher ranked you'll also often see them listed under the "cheaper alternative" section on product pages.
In comparison, CVS might see that neck pillows are really popular and decides to sell their own neck pillows and put competitor ones on lower shelves. It's quite similar behavior.
Part of the reason why the EU decides to go after Amazon and not other though, I think, is because of their market share. Amazon is huge in the EU. They hold about 29% of the market. Depending on the country, even more.
Amazon also does this on a scale that other "marketplace" type companies have not. If you ever go to the Amazon website and look under Amazon basic, you'll be surprise by the amount of stuff they sell.
The suppliers of the white label neck pillows provably made the other neck pillows. From their POV, they're largely indifferent because they've already been paid.