I know this doesn't fit the European worldview, but if only they had Costco.
They make 0-1% margin [0] on their groceries - which by the way is very high in quality.
Essentially all their profit is from their annual membership fee.
You have to buy massive quantities of everything though. This works well if you live in a huge North American house and have an SUV to transport your month's (year's?) groceries.
[0] I saw a newsletter from Ryan Reeves and confirmed it by checking their financial statements