I thought we were talking about public health interventions. How would "don't offer soft drinks, junk food, etc." be implemented? Are you going to propose a law or regulation that bans offering those things?
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.
A lot of the malnutrition of students is driven by money. For instance Coca Cola has contracts with a massive chunk of all US school districts. And schools are obviously signing those with complete disregard for the health of their student in exchange for money. But because money is the motivation, this can just as easily be fixed by executive order (amongst a million other ways). Cut Federal funding to schools that sell soft drinks or other sorts of unhealthy products to children and Coke will disappear pretty much overnight.
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.
I remember thinking it couldn't be true when the local schools first put in soda machines. Yes, banning the sale of soda and junk food in taxpayer-funded schools is an obvious, easy way to improve health. It would get major pushback from school boards which would cry about the lost funds, but they're always doing that anyway.
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.