You are correct those can be barriers/limitations, especially if you are not willing to adapt to those barriers/limitations. To my knowledge places like Schwan's still do home delivery of a multitude of fruits/vegetables, meats, and complete meals. And before you protest, Schwan's can be ordered online, by phone, or just by having a sales person stop by, and they deliver by truck, freezer bag, or UPS. Along those lines, most people can invest and should into not only a refrigerator but a small stand up freezer (most larger cities have used appliance stores and even new a freezer is only about $150 or about the cost of the smartphone you just had to have).
Instead of going out for food, let the food come to you. Another option instead of buying your groceries daily/weekly, plan ahead and buy bi-weekly or monthly. Buying in bulk (with coupons) saves money and reduces the overall time that you need for shopping so that you can reasonably plan (babysitting, taxi, friend to help, etc.). In fact, the savings brought by planning ahead and buying/preparing your own food vs. McDonald's will help pay for the items above. Invest in freezer containers and have a meal preparation day (ie. cook and then freeze the food to be reheated when the week is busy), and learn that it is okay to eat the same thing for a few days.
I agree it is not easy to be a single parent in a low income situation. However, planning and making good use of what time you do have can go a long way to take some of the pressure off your back. If you can find time to watch television, then you have time that you could be doing some of the above. I know it's not fair, but the question is, "What are you willing to sacrifice so your children can have a better future?"
But I also agree with something another poster said. Our public schools/society fail to teach us what should be considered basic life skills. No one should walk away from school not knowing basic homemaking (cooking and cleaning), budgeting (balancing a checkbook and living within your means), and basic mechanical skills (car care/maintenance, home care/maintenance). And these are lessons that should start early in education.