This would be terribly inconvenient. Living in the country, most people try to grocery shop for at least a week or two because it can be a fairly decent drive to the local grocery store.
If you had to bring your own cart then that would make it doubly hard. It'd be terrible trying to stuff a cart into the trunk of a car. lol
So I guess, there would be even more people driving trucks in the southern states.
Also have you ever tried to carry a bag of potatoes, gallon of milk, container of juice and well most anything else with it. I don't know about you, but it is just not possible for me. I only have two hands and I'm not that physically strong as a woman, either. It would be pretty difficult to make one dinner with the amount of things that I could carry, more less stock up for the week.
Just something to think about before banning shopping carts