To me, commuting is going to/from work. What you describe is going shopping/running errands.

Personally I prefer to either walk or just drive and combine as many errands as possible into one trip for greater efficiency. I lived for a long time without a car and I'm happy to not have to carry heavy things around anymore.

Some issues I see in getting people to ride bikes for running errands are: secure places to lock the bike, not looking ridiculous (hat hair, cyling outfits looking out of place in places like stores and libraries), dealing with weather that is not conducive to being outdoors, how to carry things on the bike. Also I would think major concerns would be safety in traffic and simply being physically able to cycle places, especially for many who are sedentary and/or overweight.