They are also heavier, less robust, more rigid, harder to seal tightly (without plastic), and completely impractical for large-ish items like some food items. Plastic-wrapped bananas are craziness, but a huge lot of our amazing level of food safety depends on plastics, so we can expect getting sick from food a lot more in a post-plastic world, like we used to before the advent of almost-free plastic wrappers.
I don't remember getting sick from food because it was wrapped in paper. And we still don't really know what all the hormone-like substances and microplastics leaching into our food do as a whole.