Charlie Trotter, Frontera, French Laundry, Babbo. All successful businesses. That there are unsuccessful businesses in the same category does not make them "old-school arts patronages".
The economics of celebrity chef restaurants are so different from anything else that they resemble arts patronages more than they resemble the economics of other businesses, including other restaurants.
You have to already be famous to start one, you have to have met a rich guy who thinks investing in you will make him cool, you only cater to a class of people who in previous centuries would be known as "the aristocracy." Etc.
