Earlier quoted context omitted.
It works in that given example. Of course if you invent an arbitrary number it holds no value. But the OP postulates that through force of state having safety criteria restaurants must advertise is a systemic benefit to the food service industry, and if it actually was , then restaurants everywhere would naturally adopt it if it increases consumer participation and revenues. More than anything I'm trying to indicate…
The scenario you paint isn't common for a number of reasons, but the primary issue is information asymmetry. I don't know enough about food preparation and don't have access to the kitchen of a restaurant, so I have no idea how to properly assign it a health rating. The restaurant itself can obviously produce a health rating, but if they are the type of place to skimp on health issues, it isn't that much of a stretch…
I'm not saying the restaurant itself would give itself a rating, I'm saying that if there was an economic advantage to information garnered from food safety, a private company could charge restaurants to get rated, and restaurants would seek ratings to garner customers. The fact such a service does not exist indicates that customers don't care about food safety enough to change their dining preferences to restaurants that provide such information, or else restaurants would do it, and I would be the first to line up to found that company because it would be an unexploited profit center.
> accountability and information asymmetry was GTA...
You can falsify the state of your kitchen just as much to a state inspection agent as a private one. And in both cases being caught doing it has repercussions, the former would be police at your door, the later a slander campaign by the ratings board.