When I first saw amazon restaurants (almost a year ago) I thought... meh! Why would I use this... order via phone and then wait an hour. I could order by phone call and go pick it up faster.
Turns out now we use it so much and I've found that the value is that I can order by phone when I leave work and by the time I get home the food will be arriving at my door.
The real value to me is that I can order dinner! They've had a few hiccups in the early days but now its pretty solid!