"because daily or multiple times a week shopping trips are infeasible."
Do they not have a refrigerator? Once per week trips (maybe even less) were the norm for me growing up, and I had plenty of fresh fruits and veggies.
I've lived in multiple rural areas. Yes, many people do get food from Walmart. I can see some of the more remote people preferring some processed food. I can also see those remote people growing and processing their own (canning, like I do). Many people use frozen veggies, which I don't consider processed and are nearly as good as fresh. Most of the "fresh" stuff you see is actually months old due to the way the supply chain works. It arguably loses as much or more nutritional value than the frozen stuff. This situation is completely different from the actual food deserts you get in the city. The rural people have the option to buy fresh but may choose not to. These people living in food deserts in the city don't have the option of fresh produce in the stores they go to. They generally don't have space to grow their own either. This lack of choice is the big issue.
Every area I've lived in has had farm stands and farmers markets. It has also had local stores that contract with local farmers for seasonal produce. Individual vendors/farmers do tend to have limited selection by focusing on one or two crops. But there are usually multiple farmers focusing on different things (and coordinating through the local grange). Yes, the majority of farms are monoculture soy or corn. These other farms are usually 90% that but maybe 10% other crops, like pumpkin, corn, watermelon, tomato, cantaloupe, onion, potato, honey, hops, etc. There are also CSAs that you can join for a variety of produce, including meat and dairy. My parents live in an area where the local dairy still has delivery service - that's right a good old fashioned milk man.