I cannot see it working for the family shopping trip, but going to work in good weather should be a breeze.
That depends how you do the family shopping trip. With my large panniers (and normal, non-electric bicycle) I could carry enough food for two people shopping once a week. By adding a rucksack I could carry enough for three with the small inconvenience (my back would get sweaty). A family of five might buy a cycle trailer, or get things that keep delivered, or use a taxi once a week (cheaper than owning a car?), or join a car-club.
If I'm cycling right past the supermarket on my way home I sometimes stop and buy 8 1L cartons of juice and some tins, just to save carrying them some other time. This only takes 5 minutes.