Without a backing board, a bookshelf will “rack”. That means it will lean over.
You can see this in old farm buildings. They may have been assembled with vertical uprights and horizontal sideboards.
Then age happens. Boards shrink. Snow loads. The formally vertical supports lean over. Why not?
That’s why bridges are built with triangle shapes. Some old shed doors are made with diagonal bracing. You can see it in ThomasThomas’’ss back-yard shed.
The backing board, being made of thin plywood, gives diagonal bracing. You can build your bookcase crookedly if you want to, but it’s probably easier to build it straight.
Wish that I still had some of the things that I built. I'd show you how "easy" it is. Grandpa tried not to smile. He even let me paint the "toy box". Good waste of paint. Some people can, then there is the rest of us.