a subgenre of a subgenre?

I was perusing "Shadowbridge" by Gregory Frost, and was thinking about another book I picked up recently, by Cat Valente, about an orphan telling the stories tattooed to her eyelids.

Then, I was thinking about the Illustrated Man.

Then, I was thinking about Saints and Madmen.

Then, I was thinking about a cat that took a boy through time.

Then, I was thinking about - even this one - The Name of the Wind by Pat Rothfuss of stories inside stories inside stories.

Then, I was thinking about Laputa, and the man who loved the mare.

Stories within stories within stories.

I don't recall seeing these kinds of stories inside stories inside stories in other places - just fantasy.

Is this a subgenre all its own? What do we call these? They aren't collections of stories, exactly, because they have a framing device that provides narrative arcs above the stories. They aren't novels, exactly, or, at least, they aren't *usually* novels.

Why don't these sorts of cascading frame stories seem to exist anywhere else but here?