That sounds like it's basically the grocery equivalent of the boot theory of poverty. Poor people have to pay more in the long run because they can't afford to buy in bulk.
This is exactly right and the reason that Costco shoppers are un-intuitively among the richest groups in the country (average $125,000 household income).
In addition to the other comment about perishables, storage space is another meaningful limiting factor that can vary with income level. Both the raw volume of available storage and the quality of the storage on things like temperature control, energy usage, accessibility, etc
It’s slightly different for groceries. I am not poor but I also don’t want to buy perishables in bulk. I can choose to buy one week’s worth of lettuce to be eaten in a week, but by the seventh day the lettuce has visibly degraded. I want fresher produce, so I am willing to buy smaller amounts every two days.