I feel like this ship sailed many many decades (centuries?) ago. Pretty much any store aside from small mom-and-pops will have their own brand of commodity items that they sell alongside third-party brands. Complaints about those seem to be pretty rare.
I think the difference is that the playing field is more level. Most stores that I've seen won't make it harder to buy the name-brand version or easier to buy the store-brand version (aside from the store brand often being cheaper). They tend not to really market the store brand, so the name-brand version generally has advertising behind it and is often seen as superior, even when it really isn't. The two versions sit side-by-side on the shelves without preferential placement to either.
Meanwhile, I wouldn't be surprised if Amazon gives preferential treatment in search results to stuff that gives them a better margin, regardless of whether or not it's a better product or a better value.
I don't necessarily agree that they wouldn't sell outside their own store, though. I generally look at the store brand as the usually-cheaper "generic brand". For example, if I'm looking for cold medicine, I'll never buy NyQuil, because the equivalent store brand is more or less the exact same thing and is cheaper. But I don't really care which store brand. If the CVS-branded version somehow ended up in a Walgreens, I'd still buy it. (Obviously CVS would never sell the Walgreens version, but... yeah.)
(Speaking of mom-and-pops, I actually find it annoying when I need cold medicine, walk into my local corner store, and only find NyQuil rather than the generic CVS/Walgreens/whatever store brand. The corner store usually sells NyQuil at an even higher price than the chain pharmacy would, and there's no alternative.)