You need to rethink how cities are designed for walking to grocery stores to work. It won't in the US, because everything is designed for cars. But if a city is designed right, you won't need to go miles before finding a grocery store. You can take a cargo bike to haul more things at a time. You can stop by shops on your way home from work to pick up a couple things and stick them in a backpack.

Cities designed correctly reduce the burden on those walking or biking between points of interest that are no more than 1 or 2 miles away.