why isn’t the labelling requirement something like “processed on machines that process sesame seeds” like the generous peanut one?
No idea. For whatever reason, the FDA guidelines for the law that passed requires that if sesame is present it must be explicitly listed in the ingredients list, and if a “Contains” statement is already listed after the ingredients list, sesame must be added to that list. Here’s the law in full.
Here is the consumer education material for the FDA guidelines.