Yes to Wilf and Sneak. Although restaurants that operate like this aren't quite the minority that I think you suggest. Indochine and some of the hipster joints really operate despite pans and only have nominally more online presence (simply due to the fact that people who frequent those places are more likely to go online). But to succeed that you, you need to have a cultural niche. Le Cirque certainly does. What's Romera's?
Sure, but Oakie wanted to frame the discussion in terms of expensive restaurants.