My wife has been doing the shopping with a bike for almost a year now, and I'm surprised at just how easy it is. Our shops are 1.3 miles (2km) away, and she has the whole process down to a fine art. I discovered today that she can get more into the kiddie trailer than in a shopping cart (trolley) and that despite me being unloaded, she could keep up without heavy peddling.
It is easy to wheel the trailer right up to the fridge.
Total trip time is about 10 minutes, which is about the same as driving (especially when you count the time spent finding a park and the time carrying things from the car to the house).