Urban "groceries" of all stripes would be stripped of food in a matter of hours.
Perhaps it's a matter of semantics but the mom and pop stores I referred to offered a relatively full range of veggies, limited cuts of meat,eggs, milk, butter and bread as well as packaged goods. Called them mom and pop as they are family owned and not chain stores. Pretty much the grocery store type I grew up with before the advent of the Supermarket.
Green grocers, bakeries, butcher shops, and super deli's such as Zabar's or Dean and DeLuca augment the small grocery stores. But the key thing is very, very few urbanites have more than 2 days of food in their apartments, just not enough room for large fridges or pantries.