Particularly true in US. But less so in Europe.
And worldwide, Amazon is not number one at all.
1. Taobao.com: 16% of worldwide e-commerce
2. Tmall.com: 13%
3. Amazon: 10%
4. JD.com: 8%
(source: https://www.statista.com/statistics/664814/global-e-commerce...)
The lack of competition in US (Walmart and Target took e-commerce seriously only recently) let Amazon take almost 50% of e-commerce. But hopefully Ebay, Walmart, Target and Costco would add more competition.
Painting Amazon like this only online market that we cannot escape is a bit misleading. Amazon has a long way to go to beat the asian e-commerce, and now has domestically more competition with Walmart, Target and Costco.
And Walmart is the grocery store in a lot of small towns. Amazon doesn't have that much lock-in outside of customer's preference to shop there. Their power is in that customers go there to discover products, but that's Target's advantage too and it would be weird to try and tell them how they're allowed to stock their shelves.
I think OP's point is still valid; doesn't matter if you go to one store or another (e.g., Walmart or Safeway), if that store has a house brand, chances are their equivalent house brand is at the same level or higher than the name brand.
