I also don't buy your view that the magic sparkle ponies of the market will always take care of everything. I think your approach works in theory, with infinitely smart and well informed humans. But given that we're dealing with a bunch of hairless monkeys, I think cognitive limits make it relatively easy for bad actors to push market solutions away from optimum.
More than anything I'm trying to indicate that safety ratings are not actually benefiting the restaurants if they are not adopting similar systems elsewhere. And if they had a private rating system it would only mean anything if there was some consortium that posted standards. Consider the ESRB, which is not a state review board but exists to keep states from instituting review boards in the US on video games. They specify their rating criteria in available records and are utilized industry wide because the users of the rating board find it a net benefit.
I'm not going to argue that consumers do not benefit somewhat from food safety ratings, but it is also not purely black and white, because by compelling restaurants to produce them, if they are not a market positive effect (and like I said, the lack of a natural appearance of such a system outside mandate indicates it is most likely not) then the consumer pays for those reviews with a more significant expense on the part of restaurants than the restaurants make as a result of increased traffic, which means they must raise prices systemically to compensate, and you end up paying more.
Except in a sane market, you should be able to pay more if you want to only shop at restaurants that give safety ratings from some public consortium in the first place. But then you have the choice.
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 to believe they may lie about health issues. The free market result will then be a mess. Customers who want a healthy restaurant won't know which ones are truly healthy. That makes it a hard to justify paying the premium for a health rating that could just be a lie. The restaurants then have little motivation to actually care about health since they can't prove it to their customers. In the end, you will have a market that is dominated by cheap and low quality goods (check out "the market for lemons" [1]).
The video game system is not an exact equal. The main difference is that there generally isn't information asymmetry in video games. The customer will be able to play the game and by the end of it have all the same information as the creators of the game. That provides accountability. A classic example of both that accountability and information asymmetry was GTA and the whole hot coffee scandal. The developers hid sexually explicit content in the game that was not factored into the rating. Once knowledge of that leaked out, there was a lot of backlash and the rating for the game was eventually changed.
Banking, finance, and Wall Street likely have even more information asymmetry than the food industry, hence the need for an external and trusted source of oversight.
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.
> 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.
You seem to treat that as an article of faith. In particular, you come across to me as a free-market fundamentalist. The creed seems to be something like: If a market does it, it's good; if a market doesn't do it, then it's definitionally not good. I've learned never to argue with fundamentalists, as they're impossible to convince.
Simplied question: if it is beneficial to restaurants to be forced to conform to food safety guidelines, inspections, and public ratings, it would stand to reason restaurants would naturally seek to self regulate and have their own common rating board if doing so attracted more business than it cost them to maintain said ratings.
Obviously it does not, since restaurants do not naturally do that. I'm not saying the idea of food safety mandates is good or not, I'm just saying the industry would implement it themselves if it was fiscally beneficial to the restaurants. And since it is not, that implies their rates are higher, they are less competitive as a result, and that consumers are paying for something they (in a natural market) were not willing to fork money over to see happen naturally (by way of not favoring publicly rated restaurants).