I am passionate about this issue.  I have a sugar problem; so did my mother.  I was determined to learn all I could about nutrition and break the cycle.  I did the best I could at the time with a small budget.  I was successful with my son.  I made lots of salads with cut up meats and cheeses.  I never had soda in the house, but instead bought unsweetened apple and orange juice, which I often diluted with water.  I made my own frozen fruit pops with unsweetened, unfiltered apple juice.  I had only low sugar cereal available such as Cheerios.  I used cheese cubes, raisins, bananas, and dry Cheerios in baggies for snacks on the go.  When there was an occasion like a school party or birthday party, I usually made something with some nutrition in it like Rice Krispie treats-not optimal, but an alternative. When we had birthday parties, I made my own birthday cake and it was not the focus of the party-fun and games were and there were other snacks on hand, such as pretzels.  We rarely ate any fast food.  Family members teased me when I talked about nutrition or experimented with carob or other alternative sweets, but my adult son has no cavities and is not addicted to sugar like me.  I talked to him about nutrition early on and I did not eat sweets when he was around. 
I think fast food is a cop out.  When we were kids,  fast food was canned soup and grilled cheese or a sandwich.  Again, not optimal, but much better than fast food. 
I think rather than forbidding sweets, treat them as an occasional treat.  Make time to make food at home and get the kids involved if possible (I was a working single mom).  Bottom line:  Talk to kids early on about nutrition.  Read labels and avoid High Fructose Corn Syrup and added sugars as much as possible.  Have healthy alternatives available like fruit or mustards instead of Catsup.  Start a vegetable garden with your kids.  It doesn’t have to be elaborate-you can grow tomatoes, herbs, lettuces, etc. in pots. 
Be a good role model.  Kids learn by example either way.

As a mother and grandmother I think it is a cope out. We all know if a child had any kind of illness that restricted what s/he could eat, any decent parent would move mountains to assure that child’s health. The idea we are depriving kids of the harmful junk food out there is bs. The kids will eat some junk when with friends, etc; but what they eat most of the time is what parents are willing to feeding them. It’s not what they do 10% of the time that matters. I know it is not easy, but good parenting is the hardest work you ever do. Many people just use the kids as anexcuse to not have to do make those changes for themselves