There is processed food and processed food... that is, not all the same.
You did not just hold up hot dogs as an example of good processed food, did you?
There are ways to process and deliver food without having to use known carcinogens and other extremely harmful chemicals.
Plain sugar, plain salt have been used to process food for generations until the chemical plants needed new business and looked to the food industry.
Ah well, don't listen to me. Just look at recent reports about mac and cheese products and diet sodas. The issues with these two products have been known for a long time among health experts but are now just getting out to "the public".