The idea of banning the plastic bags that we take home is to cut out unnecessary use of plastic. No one believes that the use of all plastic should be banned. This is simply not possible.
The plastic bags that are used to bag up produce do not have an obvious substitute in the way that the larger bags do. It would not be practical to put vegetables in little canvas bags and store them in the refrigerator. Therefore, those bags cannot really be done away with.
Basically, the idea of a ban on plastic bags is to do as much as possible to reduce use of plastic, not to end the use of all plastic.
On the other hand, my mother, aunts and grandmother bought produce (i.e., fruits and vegetables) that they carried in baskets or in brown bags or even in small boxes. These they stored directly in the crisper section of the Frigidaire. Fish and beef and poultry were wrapped in butcher paper and either frozen or stored in the meat compartment of the Fridge. In fact, everyone in the neighborhood shopped this way, and our neighborhood included Japanese, Chinese, Armenian, Mexican, African-American, German, and Russian citizens, so this may be seen as an international mode of shopping in the days before plastic proliferated and, some might say, corrupted our way of living and shopping and thus corrupted our ability to be healthy and steward a healthy world. These are viable substitutes, having been time and culture tested, to plastic bags in the produce and meats and poultry sections of grocery stores. Perhaps you will be the first to bring back shopping baskets or to insist upon paper bags in the produce and meats and poultry sections (though a problem with recycled bags and boxes is that they haven't yet closed the cycle with safe end-products that are toxin free--although--there has been much improvement to recycled end-product safety in the last decade).