If they did, whether it'd be something of concern would be a function of the grocery stores market size and capture.

If Walmart, for instance, were to start creating Walmart-branded everything after in-store product trials by small companies, that'd be a concern.

Walmart has done that, for decades. They have tons of their own brand in their stores selling for cheaper next to the more brand name items. Equate, Mainstay, etc. In fact, everyone does it. Target, Costco, CVS, Walgreens, etc. It is basic price discrimination / segmentation strategy.

As I said above, staples tend to have store-brand equivalents.

But you don't see Walmart creating store-brand knock-offs of every popular product on their shelves.