If Walmart is 10% of brick-and-mortar sales it's hard to argue that store brands are too competitive. 90% of that market is not walmart.
When Amazon approaches the majority of all ecommerce sales, it starts to become a bigger problem when they control the marketplace and start to undercut your products.
In general I think the fair thing to do is to make the marketplace distinction (even for store brands, which are often white-labeled third-party generics sold under multiple names anyway). You run the marketplace that allows others to sell their products, or you sell your products directly... you shouldn't be able to coordinate both as one business.
What happens when everything is free/subsidised by advertising? How do you assess the competitiveness of Facebook when they don't charge anything to use Facebook, Instagram, Whatsapp, ...
If you actually take a look at their offering (https://www.amazon.ca/-/en/stores/page/BFAE3282-E15B-47EE-90...), most of these are legitimately "basics", things that existed 50-100 years ago. Wilson won't die out because Amazon sells a volleyball, nor will Duracell because of offbrand AA batteries
This gives every non Amazon brand a massive disadvantage because they will be associated with scams.
Walmart's Great Value is exactly the same idea and is created and promoted the exact same way both in the their stores and on their website.
I think what astonish me the most is that people are opposed to something that is actually a plus for the customer. Amazon Basics is definitely one of the great thing on Amazon right now. Instead of random cheap garbage I can buy stuff that I know will be "good enough" at a great price.