No, we can't live without food. But there are a lot of foods you can live without, and when you look at the behaviors of binge eaters and chronic overeaters, it becomes really easy to identify which foods are "trigger foods," that either contribute to the impulse to binge (and are preferentially binged upon), or are incredibly easy to overeat (fuck you, pasta).
Once a binge eater or chronic overeater has identified those trigger foods, the only reasonable course of action is to avoid them, taking them permanently off the menu, the way alcoholics shun booze—because they have a similar effect.
And those trigger foods? Overwhelmingly, they are highly-refined carbs and ultra-processed shitfood that nobody needs to be eating. If you can't eat one Oreo, but end up eating the whole package, don't buy and eat Oreos any more. If you can't go through a drive-thru without feeling the overwhelming compulsion to order enough food for multiple people, which you stealth-eat in a parking lot somewhere, don't eat fast food any more. If you make a pan full of some sort of carbs-and-cheese-laden slop "comfort" food, claiming it's eight servings, only to eat all eight servings within 24 hours, stop making food like that.
Maybe cake's a problem. Maybe pasta. Maybe donuts, or ice cream, or instant ramen, or candy, or chips, or Ranch dressing, or bread, or fuck, even all of them. Once you realize that they are a problem, the only rational thing to do is stop fucking eating them, the exact same way that someone who identifies drinking alcohol as a problem stops fucking drinking it.
That leaves plenty of foods out there that will not trigger the desire to overeat or binge on them, and hey, guess what!—those tend to be healthy foods that are genuinely satisfying and good for you. Chicken, fish, beef and other red meats, green and root vegetables, eggs, beans/legumes, sweet potatoes, fruit, unsweetened yogurt, tofu (if you're into that), high-quality fats, and a bunch of unrefined grains. Oh, and you still get all the herbs and spices and onions and garlic you want, so you don't get to whine about how you're consigned to eating bland food forever.
One thing fat activists love to blather on about is how there are no bad foods, and that defining a given food as good or bad is placing moral value on it. And that's horseshit; there are plenty of objectively bad, anti-nutritive food-like products out there, and if a given food triggers the urge to binge or overeat in an individual, then it is most definitely a bad food for them, just as peanuts are a bad food for a kid with allergies.
And yes, quitting all of your trigger foods can be hard, just as quitting booze, or smoking, or any other addictive substance or behavior is. You want your dopamine hit, and you know exactly what will get it for you, and it's going to be white-knuckle time until you learn how to ride out the cravings. It gets easier. But yes, it's hard at first, and yes, your brain will keep throwing up cravings at random moments forever (I quit smoking in 1988, and still get odd cravings for a cig, now and again), but if you really want to free yourself from your addiction, you can do it.
