The small menu is so appealing and the place itself so charming that you almost forget, as a diner, that you have to do much of the work of dining out yourself. You scout your own table. You fetch and fill your own water glass. And if you’d like another glass of wine, you go back to the counter. A lot of low-range restaurants work in Australia and New Zealand. Is this really that rare in America?
I also know of a place near me where you order at the counter, and someone brings you your food when it's ready, but they don't "wait on you" beyond that.
Panera (sandwich & soup chain) used to have you order at a counter and collect your food when it was done, but they have been trying to get people to use touchscreens for ordering, and take a radio homing device* to your table so you can be brought food by the people who used to take your order.
*where the low tech solution that would work just as well is to simply ask your name when ordering.