There was a point where tires were expensive but they lasted a long time because so few people had cars and they didn't drive them often. So two brothers who owned a tire company were trying to figure out how to sell more tires to the few people who owned cars.

The answer was to get them to wear their tires out faster by providing a list of places they could visit that would warrant the expense of wearing down their tires.

So the stat rating was more of a "this place is worth a visit/road trip system. And they published this list and it caught on and then restaurants wanted to get Michelin stars for the notariety and the essentially free press.