One thing I like about Japanese stores, they ask you if you want a bag....partly because they charge you for it (typically 3-5 Yen). For small objects at a convenience store, I often skip the bag. I typically carry my own fabric bags for deliberate grocery shopping, but if I forget I spend the few extra cents, and typically re-use the plastic bags around the house, usually as intermediate trash bags.

I think an outright ban is overkill.