I have a friend whose family of five is car free and he does big grocery runs with a hiking pack or even bike trailer.
But certainly point taken— that type of thing is well outside the norm. Most carfree urban dwellers I think handle this by just breaking up the shopping into more, smaller trips. Going every two days instead of every seven, and paying a slight premium for smaller packs of stuff like TP vs stockpiling 48 rolls at once.
And honestly, some of it is a mindset shift more than anything else. Like a lot of people who do these big whole-week mega shops still seem to be "popping out" to the store (in the car, of course) every other day anyway for some single item they forgot, emergency snacks, whatever. So maybe if you're there anyway, do the work and extend the meal plan another day or two, bring a backpack’s worth of stuff home, and avoid or defer the mega shop that justifies owning a car in the first place.