I happen to be against too much government interference. Thus I would never suggest we do anything to regulate sugars. But, since we are all paying the higher health care costs, we should as a society fight it with clear, unbiased research. For over 50 years, we've been quietly steered into researching the wrong problem:
https://www.nytimes.com/2016/09/13/well/eat/how-the-sugar-industry-shifted-blame-to-fat.html?_r=0
It is no wonder that people don't follow nutritional guidelines very well as they were biased from the start. How many times do you hear of some food that was bad is now good or some food that was good is now bad. We can and should support truly independent research into the real causes of health problems. Then, people would start having confidence in our nutritional guidelines and might eventually start following them more.
I'm also all for limiting refined sugars in government supplied foods. Soft drinks are the #1 purchased food items for people who get SNAP (food stamps). Even if SNAP doesn't cover Coke and Pepsi, people just buy their regular foods with SNAP and then behind that use their own money for soda in a separate purchase. How about doubling the SNAP benefits on non-sugar based drinks so they buy healthy drinks with SNAP? Then they don't need the soda as much. Same goes with school breakfast/lunch, prison foods, etc--provide more tasty and healthy alternatives so that people don't need to resort to the refined sugars.
It's definitely a complex problem. Government interference is a bad answer, but the govt can usually put pressure on certain unhealthy industries as it's done in the past. Taxation has been the favored tactic, used for alcohol/cigs (and sugared drinks by some state governments). One could argue that the government should step in if it's provable that there's a psychological component (addictive quality) which is encouraging the continued 'use' of the 'drug', as it were. Note that I'm not stating that sugar is a drug, only positing a scenario.
More and better education is definitely a key component here, as the vast percentage of heavy soda drinkers are likely following their parents 'because that's what they've always done'. I personally know a family (relatives) among whom the entire household drinks soda for every meal, breakfast included. It's basically a substitute for water.
SNAP shouldn't cover sodas, I agree. It should only cover required subsistence, preferably nothing packaged outside of maybe pastas. In fact it could be argued that in lieu of providing cash for food, the program should simply provide the food (in the form of MRE's maybe?), but that's probably far less efficient for the money.
The schools, prisons, etc all run into the same problem: commercialism/capitalism. School/prison isn't getting enough money, Pizza Hut offers scratch for a kiosk within the cafeteria, School feels obligated to not leave money on the table, cafeteria now serves (expensive) pizza alongside cheaper, and more healthy 'boring food'. 50% of the school population is now eating pizza every day for lunch. That is exactly what happened to my school back in '99/'00 or so.
How do you halt this without a) government intervention, b) carpet bombing information campaign (which may end up shut down by lobbying)? Plus, B at best leads to a bunch of crunchy granola health hippies, and nobody wants that.