I haven't seen this particular type of repair in an Ithaca Flues gun. I do see quite a few Flues that have pieces of wood missing at the top of the stock head on either side of the top tang, directly behind the action. I also see some that have been repaired in that same area, and have repaired a couple myself. One Flues I bought very cheap had boars tusks screwed into the wood in place of these missing pieces of wood. Talk about a Bubba repair! I believe it probably happens due to recoil battering on the old brittle wood when the action gets a bit loose in the stock.
I find it very interesting to hear that Fox used these corrugated reinforcements as a factory solution to a problem they obviously recognized early on. The type of repair you picture here is also pretty common in other guns. More often, a broad metal staple is made to bridge the crack in the center of the stock head, and is there as added reinforcement to any glue or epoxy repair to prevent the crack from opening back up. Properly done, it works very well to save original wood. Some guns, such as Parkers and Remingtons, are a bit worse in this regard than others due to their wedge shaped tapered tangs. They were likely OK with the vintage loads for which they were designed, but things like age, stock oiling, loose screws, and battering from heavy modern loads cause them to split.
Unfortunately, there are much worse Bubba repairs done to these guns. You often see them with dowels, nails, wood screws, and even stove bolts fastened with farmers nuts through the cheeks of the stock. Then there's the gray epoxy and baling wire repairs. The so-called "staple method" is at least hidden, and therefore more aesthetically acceptable. As with many gun repairs, there is a right way and a wrong of doing it.