I also wondered if they didn't just start labeling as such since they couldn't guarantee that things didn't get contaminated with sesame. "This product is made in a facility where sesame is used"...even if we didn't use sesame in this product being the unwritten part.

That's literally exactly the reason why they did it. They made their food in a factory that also has sesame, and instead of building an entire new factory for only one item (which is expensive and might not even be financially viable in some cases), some companies did exactly that due to the FDA regulation change.