I have been telling my spouse "stop buying junk food" for literally 15 years, without interruption. Every time, the response: "yes, I know" when agreeable, and "what constitutes 'junk food'?" when contrarian. It still somehow shows up in the house all the damned time. I'm not going to place the blame entirely on someone other than myself, because I do eat the crap instead of throwing it in the trash, but can I really threaten separation over one box of brownie mix? Is it any more reasonable to split over a thousand boxes of brownie mix?
We both know how to cook--perhaps a bit too well. Even if we didn't buy boxed brownie mix, we could still make brownies from staple ingredients and a bar of baker's chocolate. Or cookies. Or pies. The difference between us is that I refrain from doing so. You really have to take away the bag of refined sucrose, and the bag of white flour, too. And then you have to take away the corn, rice, and potatoes, because some impoverished ancestor figured out how to make "sweets" (read: black-market booze) out of the cheapest starch available, and if you stop short of the fermentation, it's still not-entirely-disgusting to eat as is. "Stop making junk food" is taken a bit too personally.
As I am not a peasant farmer that works heavy manual labor for 12 hours a day, there is no amount of exercise I could squeeze into my schedule that could compensate. I could stop myself from eating it, of course. I could quit at any time I wanted--probably without even checking in to rehab.
What you need is to know how to cook just enough to heat meats to the correct internal temperature, steam vegetables so they are neither crunchy nor mushy, and make vegetable soup, and then also not have the ability to make things more delicious with added fat, salt, and sugar.
Food deserts may be a thing, but that is also because the more nutritionally-dense-per-kcal fresh produce is expensive in relation to the boxed and canned junk foods. And some vegetables cost more than others. A 10# bag of potatoes can cost less than two heads of cauliflower. A 20# bag of white rice can be less than 2# of brussels sprouts. Carbohydrates are simply cheaper than vitamins-in-foods. If you can't afford a car to get to a grocery store on demand, you can't afford to replace all your junk food with fresh produce, either.