Study author did a comparison of restaurants reviewed by the NYT and ones that got a star over almost 2 decades (2000-2019). Found that restaurants that got stars were significantly more likely to close than ones which had simply got positive NYT reviews. Lot of hypotheses about factors that could cause this drawn from interviews with chefs/owners and other analysis. Upstream vendors, and landlords increasing prices to try to capture some of presumed extra revenue the restaurant would be making or needing to pay staff more because their profile is higher. Downstream, different expectations from diners leading to higher costs, more diners who aren’t local, etc.
Study seemed pretty rigorous and is linked below. Interestingly the higher your NYT review rating, the better your odds of staying in business in contrast to getting a star. It’s pretty difficult to show causation, so take the results with a grain of salt. It did seem like there was a pretty strong correlation between getting a star and higher chance of subsequently closing.