Surely all glue is edible, you just have to commit a bit more to some glues than others.

It's like that saying about mushrooms: "All mushrooms are edible. It's just that some mushrooms you only get to eat once."

Elmer's white glue is "non-toxic" but today, it is made with synthetics. Since my youth in the early 80s, Elmer's has never been particularly appetizing or appealing to put in my mouth.

I believe that the stereotypical "craft food" is actually paste, which is often based on starches like corn or wheat. Children are very likely to put paste in their mouths and try eating it, because it is indeed based on food products.

I've frankly never been in a school that provided a lot of paste, and the switch to Elmer's glue may have been a strategy to stop kids from consuming the food-based stuff. However, I was in a summer science course where we crafted "Oobleck" which is also sort of "edible" if you like eating clay that's been squeezed between the filthy little hands of 8-year-old boys.