You're totally right, the product exists, but access is still a problem. Mobility is a tremendous issue to people in poverty, which is as intended in some cities with populations with large wealth gaps. If a family has one car, the person working may take it for the day for work, leaving everyone else at home with only their feet or public transportation to get around. Unless they can purchase cheap produce in their neighborhood, it may take hours to get to that place, buy what they need, and return before it can be prepared. Imagine taking a bus to Costco to do the weekly shopping (payday dependent, in this context). Certainly if their life is planned around this event it becomes more reasonable, but it will be less convenient than walking to a corner market or local fast food joint and spending a few dollars to feed everyone.

Have you ever had your car break down? Last winter, mine did less than a mile from my house on the interstate in the middle of the night, and I was completely stranded. Relatively, I travel hundreds of linear miles a month and have never felt that way, because "I'm only ever a few hours away from home." Your world gets a helluva lot smaller when you don't have mobility, and anyone who doesn't appreciate that really can't understand the problem with calling pulling up farmer's markets in a 20 mile radius on Google a solution.