Experiments concerning the effect of publishing calorie counts on restaurant menus tend to show little effect on choices. In the experiments that I know of, choices before and after publishing calorie counts are compared. But this form of test cannot be considered conclusive. Some people were overestimating the calories and they might cut back, some were underestimating and they might eat more. There is no reason to expect that the aggregate change should be positive or negative.
A better experiment would be to use a restaurant where calorie counts are already published and manipulate them. Will people change their choices when you add 5% to the reported calories? 10%? What is the elasticity? It’s a safe guess that there would be little response for small changes and a large response for very large changes. Any response at all would prove that their is value is publishing calorie counts because it would prove that this information is useful for choices.
The only question that would remain is how those welfare gains measure up against the cost of collecting and publicizing the information.