Convenience stores aren't really more expensive small grocery stores. I'd challenge you to regularly pickup the ingredients for a tasty healthy dinner from a typical US 7-Eleven.
Our local equivalent has bacon wrapped steak, potatoes, with some avocado on the side.
Or you can get the 1.5 lbs of chicken breasts (boneless) for $7.
Of course I’m actually only a block from a normal grocery store so I don’t need to worry.
If you're lucky they may sell not quite ripe bananas at the front counter. Otherwise the healthiest is going to be cheese from the cooler, orange juice, and tortilla chips.
Ours adds carrots, lettuce, avocados, apples, oranges, potatoes and sweet potatoes, along with other stuff I can’t recall.
This s 7-11? I may have seen a few with a wider selection, now that I think about it.
Independent stores sometimes are better, sometimes worse.
Of course NYC-style bodegas are a completely different thing, but you don't see that outside of the biggest and densest cities.
We do have "convenience stores" some of which are effectively very small grocery stores (produce, fresh meats, etc). But usually significantly more expensive.