It's also been done in actual reality. For example, one of Sweden's largest supermarket chain is the consumer co-operative Coop [1]. Their own line of budget private-label products had a very minimal "no-brand" design, though in 1979 they started using the name "Blåvitt", referring to the blue-white colors of the minimal design. I found a picture [2] of some of their products (coffee, detergent, tooth paste, tea, soap, bread, etc).

[1]: http://en.wikipedia.org/wiki/Kooperativa_F%C3%B6rbundet

[2]: https://fredrikedin.files.wordpress.com/2009/12/blavitt.jpg