> the disadvantage might be more about how grossed out people might become if they realize how old some of the food on the shelves might be.
Only if you've never knew that before? I mean, I guess that's true: I know that e.g. cereals and past can go for years if store properly but if you never knew that, it may shock you. But if for you whole life you've seen labels "Shelf time: 18 months" on various foodstuffs, that's just the piece of general ambient knowledge.
> if they needed to also include the origination dates of each ingredient, recursively
Well, this is ridiculous, so they are not required to do that although, of course, there are (self-)regulations on how old can the ingredients be for the manufactirers to be able to claim the shelf-life they want to claim.