Couple of issues with paper bags. They don’t hold up under rainy/wet conditions and they are much more likely to harbor pests.
One neighbor during my time in Boston had to have his entire apartment fumigated after having no previous issues for nearly a decade living there because it turned out some paper bags he brought home from a supermarket harbored some roaches. That was confirmed after the exterminator fumigated and investigated the source of infestation and the neighbor found several other shoppers had similar issues around the same time frame.