Grocery stores are pretty low-margin, and need a certain amount of demand (for the size Americans are used to).
Some convenience stores get moderately close to being a grocery store.
It'd be an interesting experiment to see how few products you could carry (and of course, only one of each type) and have people still willing to shop there.
American-sized grocery stores are relatively new though. When I lived in Germany downtowns had plenty of smaller, specialized stores. There'd be several small butchers, small bakeries and sometimes even a fish monger. Stores that carried produce would usually beer less specialized but there still would be plenty of small ones like Spa and Edeka used to have small locations in walkable areas. And of course proper markets at various frequencies.
Some convenience stores get moderately close to being a grocery store.
It'd be an interesting experiment to see how few products you could carry (and of course, only one of each type) and have people still willing to shop there.