I started laughing when I got to this. I wanted to build stuff even though I was a girl. Grandpa tried to teach me. And tried. And tried.
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.
Even your kids are 'half-a-bubble off'...