I met people in London who also pay people to grocery shop for them. For most staples I'm pretty sure this could probably be cheaper then having a grocery store in SF, they could have a warehouse in Fremont.
(I agree though, I think this is something that is going to happen - just have to find the right business model at the right time.)
From what I remember I've seen quite a few "night time delivery only, no pickup allowed" grocery "restaurants" on those services
I am not sure why they failed but more recent attempts seem to be succeeding. My two current theories are: 1. They were ahead of their time. There weren't enough people shopping on the Internet to sustain them back then. 2. They were killed by structural obstacles that may also kill the new versions.