Yeah, 2 miles is ~80 minutes round trip on foot for a healthy person. 5 miles is over 3 hours round trip on foot, carrying groceries back. This is not accessible.

If a person is poor enough to qualify for food stamps, is it reasonable to expect them to have enough land and resources (fertilizer, etc.) to grow enough food for a family, while also earning a living? Should that be the only option?

Finally, of the group of people who do not have reliable access to cars, the poor are a significant portion. "Just jump in your car and drive down the road" is not an option for millions of Americans.

But yes, if you are relatively well-off, there's no such thing as a food desert. If you have a few tens of acres of land, a tractor, and car, even being 50 or 100 miles from a store is not a problem. SNAP isn't for those people.