If you've been to New York or heard about its urban form, you probably know that many, perhaps most, of the supermarkets in the city don't have parking lots. People just walk to them. Maybe you're thinking: that's impossible, a car is necessary to transport groceries.
There's a very simple solution to the problem of carrying a bunch of stuff as you walk.
That's right. Everybody just gets one of these carts. They fold up and attach to supermarket shopping carts. Think about that. We're so pathetically dependent on cars, that we've forgotten how people used to live without them.
If you live walking close to a grocery store (you almost certainly will in a dense city that mixes land uses) and have one of these carts, carrying groceries is no problem. There is an issue in the city of buildings with no elevators, but that's a housing problem that I feel isn't fair to blame on the concept of a dense, mixed use city.