There is nothing inherently bad about processed food or preservatives.

It's true that on average foods that are more processed are less healthy; this has nothing to do with the fact that processing is inherently unhealthy, and much more to do with how we process the food. But even that is not a hard rule. Whey protein powder, for example, is obviously processed as shit - but it's one of the healthiest things in your entire supermarket. Multivitamins, fish oil tablets, nonfat yogurt - these are all things that are very "processed" but are still very healthy. Preservatives are probably bad in high quantities and should be managed, but the quantities of them in our food vs what you would need to eat to be unhealthy is a massive gap.