True these polyurethane bags are definitely a mess and like you, I also think likewise. However, your idea is not practical for several reasons. When it comes to food items, people would not like their food to packed in used bags simply because one would not know how badly the bag was used by the previous user. What I usually do is that I carry a bag from my home whenever I go to the Baqala. I am possibly the only one in my area who does this and the Baqala people smile and appreciate my act. It is my very small way of contribution. However, this act cannot be practised at large supermarkets as the supermarkets shopping bags with their logos on is form of security check. Security people at such markets keep a watch for their own bags.
There is no way to ban these bags. There are two factors behind this. First is the cost. They hardly cost anything. Second is the convenience.
My country did take the step of banning it. It led to brawls between customers and shopkeepers on almost a daily basis. Ultimately, the regulation on the ban failed.