"Your stores are going to have to be as big as a supermarket to really be of use to people."

Not necessarily. You could make more efficient use of space if you don't have to arrange the store to be customer-friendly.

"I don't even need to go to the store then, they just get delivered to my front door. Or do supermarkets not do this in the US?" Most places, no. Where they do, it's more expensive.

"Personally I've never felt that online ordering has saved me much time."

It certainly could if it were done well. Don't you normally buy a lot of the same things? A good interface would remember that and help you reorder favorite items quickly. Also, groups of items - "all the stuff I need to make recipe X." The store could even upsell by suggesting a recipe and selling you all the items you need to make it, then including a printout of it.

Think how quickly you could shop if you could specify the meals you want to make this week instead of looking for each item individually.