As annoying as the answer might be, that logic just doesn't work for large populations and densely populated areas. Some perspective, I've lived in and helped manage a student-run co-op of 50 for 2 years now. We have chickens, we have a garden, we have some sort of aquaponics project that still hasn't gotten itself off the ground. It's nice when I can walk out and grab mint for dinner. The cherry tomatoes we grow on the roof are delicious. I'm not a fan of the eggs (there's usually poop on them), but they do get eaten. At the end of the day, however, the gardens get plucked by deer and small rodents, the chicken coop now harbors a rat's nest, and we realistically end up buying 99.9% of the food consumed by the house. Food politics is a big thing here, and for a while I was told not to buy bananas for the house because members considered them unethical. But I've grown largely cynical of home-grown farming endeavors. They just don't work out when the number of inhabitants of a plot of land exceeds 10. In suburban and rural areas, that's fine, and it's a beautiful experience to watch organic matter rise from the ground and become food, but in apartments in cities, they serve little purpose past distracting passerbys from the bleak meaninglessness of life.
You're completely right. It does not work for urban areas. But I have a personal belief that the modern megacities are essentially pathological, just by virtue of being too dense. I believe that to improve the lives of the most people we need to, over time, depopulate cities a bit, and push more people out into essentially neo-villages, so that each populational unit is almost self sufficient with regards to food, medical services, education, and utilities. We'll always have cities, but I think that living in them will be considered a temporary inconvenience when compared to my utopian vision of small towns full of scholar-farmers.