A decent weekly shop yields over half a dozen supermarket bags. Don't get through anything like that number of bags.
Our council supllied bag takes us a fornight to fill. Only goes out with the recycling collection every two weeks. All it contains is plastic wrappings, everything else goes to recycling or the compost heap.
Half dozen of the check "laundry" bags a number of years ago, still going strong and have at three or four times the capacity of a freebie supermarket bag. As they are fairly rigid and rectangular they sit nicely together in the boot.
No handles so no carrying 2 or 3 in each hand. The give way if they get damp.