publix, a florida (and now georgia too) grocery store had what they called publix direct a couple years ago. you would go online, purchase your groceries and then they would be delivered to your home. they charged a delivery fee (i'm not sure what it was) but needless to say it didn't last very long. they found that people preferred going to the store to do their shopping, so they cancelled the service.
personally, i enjoy grocery shopping so i wouldn't pay anyone to do it for me.