I remember the time when everyone used their own bag, and anyone who went shopping without one was considered as feckless as a meringue who enjoyed walks in the rain.
When did it become a right to have someone else provide it? Why should the supermarket provide carrier bags for the unprepared? Small plastic bags for dairy produce, fair enough, but if you are buying more than you can carry in your arms, surely you have enough prior warning to pick up a bag before you shop?
A folding bag in a pocket or handbag takes up almost no room, and a more substantial one can live in the car boot. I have no car and have to carry home shopping in a bag or backpack, or wheel it in a shopping trolley. If I relied on flimsy plastic bags with knife-edge handles my hands would be cut to pieces, so I keep a light bag with sensible handles in my handbag - it is a no-brainer.