Anything over 3 lines of ingredients doesn't go into our shopping cart - and then it has to have a good reason with 3 lines.
It's up to parents to educate kids in healthy eating. To reduce the battles, just don't offer the junk in the first place. My daughter is very picky, but also has no idea what most of the junk tastes like. Our battles are much narrower - along the lines of 'fish with mashed potatoes, OK - are you going to try broccoli or peas with it?'. We're far from perfect or winning the game, but we've made the rules much easier for ourselves.