That's my point; if you look at a map of obesity rates in the US overlaid with a map of poverty, there's a very strong correlation.
The cheap access to calories today makes it easier to overconsume. In the past, the high cost of calories meant that only the wealthy could really ever become obese (outside of genetic factors).
But even if absolutely true, how do you solve for that? Laws limiting what you can purchase/eat would simply be a non-starter.
It would rankle some people, but so do taxes on alcohol and nicotine. My big concern is that I'm skeptical whether we can really identify those "bad" foods and that even if we could whether we could ensure the government would whitelist/blacklist the correct foods.
As far as lack of control goes, I'd be curious if fatter/poorer people would do worse on some kind of adult marshmallow test. Maybe see if you can get them to sit perfectly still for 20 minutes in exchange for a monetary reward. I don't have a strong sense that they'd do worse than skinnier/richer people.
One hypothesis is that this is due to "food deserts" where the lack of access to fresh foods leads to over-reliance on processed foods for caloric needs.
It is no coincidence that there is also a strong correlation between food deserts (at a national and local level) with lower income. The solution probably isn't banning specific foods, but to solve the access problem and address socio-economic factors. Better health and nutrition education may also be key.