Another thing is to remove the ability to purchase junk foods and cola with government food assistance. There's an extreme inverse correlation between obesity and income (hah.. imagine people of a couple hundred years ago hearing that) and so steps like this could actually have a tremendously positive overall impact on overall social health and wellbeing. This is even more true when you consider that twinkies and cokes are being bought on strictly limited budgets which means that much less money (and now more) for healthy foods.
There's merit to the government food assistance (SNAP in the US) idea, though if you're trying to ban "junk food" from SNAP you're going to run into definition issues. Banning things like Twinkies and cola from SNAP is one thing, but "junk food" may also include ready-made ultra-processed food depending on your definition, and that may be the only type of food typical SNAP recipients can use (e.g. homeless who do not have access to cooking, people who live in food deserts). There is also a valid concern about micromanaging the food people eat, because SNAP recipients are normal humans and we tend to give normal humans leeway to indulge in a treat every now and then.
Food deserts are largely irrelevant. Things like rice, beans, canned goods, and other such products are widely available and provide sufficient nutrition. There is also online food ordering (from Amazon etc) that allows payment with things like SNAP. And the sort of products we're talking about are not "treats", and should not be seen that way. They are highly addictive and harmful trash that, in the future will almost certainly be completely banned, certainly in anything like their current formulations.