I agree, low carb is very important for controlling food addiction, because it takes away physical desire for food and it kind of robs food of its power as a drug (one that can influence moods, one with a long history of deeply ingrained instinctual behaviors in response to the former).

So then at that point you're physically detoxed, and you're not eating "trigger foods" (foods that resemble/remind you of old behavioral patterns, even if physically they are not harmful)... and all you're left with is the "void" left by not having food anymore. Then you have to deal with that, which is in a lot of ways more difficult than learning to fix the carbohydrate sensitivity. There is a mourning period for food addicts (or at least for me) where you are missing being able to eat all the time. You feel emotionally "flat", in grayscale, not as alive as before. This is why I think a lot of food addicts relapse, because beating the addiction is akin to losing a friend. Your capacity to experience life in color, emotions, to just have fun is compromised by cessation of food abuse.

I think food addiction is what happens when a pre-existing carbohydrate sensitivity unfortunately coincides with a certain emotional/intellectual temperament. It develops by a carbohydrate sensitive person learning that food has an unusually medicative property on the body and mind. When someone who has a sensitivity to carbohydrate ALSO happens to be very emotionally extreme, sensitive, perceptive, nervous, and introverted by personality ... food abuse is very likely. The powerful effect food has on their body, combined with and emotional/intellectual orientation, results in an abnormally strong relationship with food developing usually very very early in childhood. People who think hard on things, and feel things deeply, are more likely to develop relationships and be affected permanently by things that have a powerful affect on their senses. For the carbohydrate sensitive person, food has the ability to totally affect the way you feel emotionally and physically like drugs do.
When this person - emotionally sensitive, nervous, and carbohydrate sensitive - grows and develops, they will as a consequence of repeated conditioning be food obsessed. Food will be enjoyed the way a normal person enjoys other people. Food will be their best friend. Food will be elevated to the status of being more than inanimate, it will be the focal point of all celebrations, all life experiences, all upsets, every waking moment will center on it. Food will become your primary reason for living.

If they don't become active food abusers (compulsive/binge eaters), then it's very likely they might develop bulimia or anorexia or some other form of disordered eating instead.

So I definitely agree that a true food addict is someone with carbohydrate sensitivity, and therefore a low carb diet is for most all food addicts crucial in keeping it under control. However, the relationship and habits and behavior that evolved around living life with that sensitivity is far more harrowing than simply choosing extra cheese in lieu of 2 slices of bread. Learning how to truly live, cope with, and enjoy life in a context without the crutch of food abuse is extremely difficult if not impossible.
Whether or not the fake foods help depends a lot on the nature of the problem. For me, they helped a lot. My M.O. with food was to eat everything but to not feel a compulsion to eat the entire contents of any one thing (this is likely because I was raised in a household with lots of people, and having a container of food all to myself was not practical... taking a big portion of everything, on the other hand, was the way I indulged my insatiable need for food).
Now whatever was on my plate I DO and DID have an irrational compulsion to eat... but I did not have to eat the entire box of cookies or the entire pizza, or the entire contents of anything that was meant to serve numerous people. This was because, like I said, the foods I ate were "family foods" and I never developed that habit. The way I coped with my carbohydrate sensitivity (the bad habits, which became emotional compulsions, that I learned from it) was to take huge portions of as many foods as I could.

I think food addicts who were raised as only children, OR food addicts who were put on diets (and therefore prone to buying/stealing food to consume in private) are much more likely to feel a need to consume the entire contents of a family sized container of food.

If you have that need to "finish it all" then it's likely the fake foods are only going to trigger you to want to eat the whole thing. If you're like me, and consciously preventing your tendency to take big portions from being a problem... you CAN indulge in your desire to have a little bit of everything all the time. I am lucky that my problem was mainly with portion size, and once my "serving" is taken I have very little problem stopping. It makes me very thankful I lived in a crowded house where dividing desirable food into portions was standard .