We are mostly on the same page I think. To the point though, re: food - it is not all equal. Fast food, ice cream, fried food, candy, chips- it is quite different from cooking your own meals and snacking on things like fruit, veggies and hummus (etc..)
Similar to your first point, I can't buy ice cream because I have no self control over it. (I would not say I have a food problem, it would therefore be a lot harder for others I believe)
While I agree "you can't abstain from food", it might be a bit overly reductive. Not all food is responsible for 'problem' eating. Similar to near absolutely (or absolutely) avoiding booze/nicotine, there might be similar foods that must be avoided. Which comes back to habits, changes to how a person snacks, when they eat, how long is spent in food prep,more grocery store trips, how they shop in the grocery store (etc)
If the same logic applies to a "food addiction", then discontinuing the drug that helped you go over the initial addiction is going to be almost impossible, since you can't abstain from food.