It’s funny. I thought the design was going to require horizontal support across the back to prevent racking, particularly since there’s not much holding the shelves in.
I was going to glue and screw battens across the back.

But, after gluing the shelves in, it’s rock solid.
Since I had already milled them, I glued two pieces across the back—basically, so Mrs wouldn’t have to worry about pushing her binders in too far.