Over here (UK) the corner shop often has some fresh fruit, veg, milk and bread. They are of course more expensive, but in my opinion, the extra cost is not huge for one or two meals worth of food, especially laid against the angst and ennui of a heavy traffic supermarket!
Yeah, you're lucky to find any produce at all in an American convenience store, though you're likely to find milk and probably bread in the better ones. On the other hand, there's all the beer, soda, "potato chips" (crisps to you), and chocolate bars you could ever want; sometimes a better selection than the supermarket!
Also, because Americans drive everywhere and walking is impossible in most places, most of our convenience stores are attached to gas stations (petrol stations to you).
Large US cities have plenty of neighborhood markets / corner stores with fresh fruit and vegetables and meat. I live next to 3 of them in West LA, within walking distance. SF has even more. NY has countless. And yes, they are much more preferable and expensive than supermarkets. The markets in California usually have world class wine and produce, since our state grows millions of tons of the stuff.
But yeah, most American suburbs don't have any of that, which is what you're describing.
"Consider the Lobster" and "A Supposedly Fun Thing I'll Never Do Again" are collections of his essays. They're still fairly long, but they're generally superb, and you can read them in smaller chunks than his novels.
PS: Do you not have corner shops in the US?