Why would you transport a week's worth of groceries in the first place? In cities designed not for cars, most people generally don't "transport" groceries at all, since everybody generally buys groceries very close to home (often on the same block), and the natural time to do it is on the way back from work/studies/whatever, so instead of having an explicit weekly trip, you just buy whatever you need now or for tomorrow, not a week's supply - and that is easily carried (not transported) for that short distance even for a family of 6+.

If you buy something that can't be carried, like a refrigerator, well, then you get it delivered.