Banning food from some places might help - I am surprised at a university library allowing food - I don't think I was back in the days I was student. Too much of a risk of damage to the books!
Taxing food, on the other hand, won't.
Who decides what is unhealthy? The vast majority of food is OK in moderation which is the key -it is about portion size and getting the balance between the very nutritious and the less nutritious correct. As I said earlier, diary products are high in calories and saturated fats, are you going to tax those too even though they have nutritional value? Carbs like potatoes, rice and pasta are all healthy in moderation but if eaten to excess will make you fat, whether they are brown or white versions, because they are high in calories.
And if you can't decide what is healthy and what isn't, what do you put in those shops which only sell junk food? It isn't about good food and bad food - I have seen people who eat a seemingly healthy diet and have very few empty calories but they are still fat because they have no portion control and they don't know when to stop. Banning junk won't help them because they don't eat it. We are simply eating too much as a society relative to the amount of activity we do. The balance between what we put into our bodies and what we expend has gone.
Banning things and restricting them only makes people want them more. It is basic psychology. You have to find other ways getting people to make their own decisions on healthy eating.